[1] M., Ajtai and Y., Gurevich, Datalog vs. first-order logic, Proc. of the 30th Annual IEEE Symp. on Foundations of Computer Science, 1989, pp. 142–147.
[2] D., Archdeacon, A Kuratowski theorem for the projective plane, Journal of Graph Theory, vol. 5 (1981), pp. 243–246.
[3] S., Arnborg, D., Corneil, and A., Proskurowski, Complexity of finding embeddings in a k-tree, SIAM Journal on Algebraic Discrete Methods, vol. 8 (1987), pp. 277–284.
[4] S., Arnborg and A., Proskurowski, Linear time algorithms for NP-hard problems restricted to partial k-trees, Discrete Applied Mathematics, vol. 23 (1989), pp. 11–24.
[5] A., Atserias and E.N., Maneva, Graph isomorphism, Sherali-Adams relaxations and expressibility in counting logics, Electronic Colloquium on Computational Complexity (ECCC), vol. 18 (2011), no. 77.
[6] L., Babai, Moderately exponential bound for graph isomorphism, Fundamentals of Computation Theory, FCT'81(F., Gécseg, editor), Lecture Notes in Computer Science, vol. 117, Springer-Verlag, 1981, pp. 34–50.
[7] L., Babai, Graph isomorphism in quasipolynomial time, Proc. of the 48th Annual ACMSymp. on Theory of Computing (STOC '16), 2016, pp. 684–697.
[8] L., Babai, P., Erdös, and S., Selkow, Random graph isomorphism, SIAM Journal on Computing, vol. 9 (1980), pp. 628–635.
[9] L., Babai and E. M., Luks, Canonical labeling of graphs, Proc. of the 15th ACM Symp. on Theory of Computing, 1983, pp. 171–183.
[10] J., Barwise, On Moschovakis closure ordinals, The Journal of Symbolic Logic, vol. 42 (1977), pp. 292–296.
[11] J., Barwise and S., Feferman (editors), Model Theoretic Logics, Perspectives in Mathematical Logic, Springer-Verlag, 1985.
[12] C., Berkholz, P., Bonsma, and M., Grohe, Tight lower and upper bounds for the complexity of canonical colour refinement, Theory of Computing Systems, vol. doi:10.1007/s00224-016-9686-0 (2016).
[13] H. L., Bodlaender, Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees, Journal of Algorithms, vol. 11 (1990), pp. 631–643.
[14] H. L., Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth, SIAM Journal on Computing, vol. 25 (1996), pp. 1305–1317.
[15] R. B., Boppana, J., Hastad, and S., Zachos, Does co-NP have short interactive proofs?, Information Processing Letters, vol. 25 (1987), pp. 127–132.
[16] J., Cai, M., Fürer, and N., Immerman, An optimal lower bound on the number of variables for graph identification, Combinatorica, vol. 12 (1992), pp. 389–410.
[17] A., Cardon and M., Crochemore, Partitioning a graph in O (|A| log2 |V|), Theoretical Computer Science, vol. 19 (1982), no. 1, pp. 85–98.
[18] J., Carmesin, R., Diestel, F., Hundertmark, and M., Stein, Connectivity and tree structure in finite graphs, Combinatorica, vol. 34 (2014), no. 1, pp. 11–46.
[19] A., Chandra and D., Harel, Structure and complexity of relational queries, Journal of Computer and System Sciences, vol. 25 (1982), pp. 99–128.
[20] B., Courcelle and J., Engelfriet, Graph Structure and Monadic Second- Order Logic — A Language-Theoretic Approach, Cambridge University Press, 2012.
[21] B., Courcelle and S., Olariu, Upper bounds to the clique-width of graphs, Discrete Applied Mathematics, vol. 101 (2000), pp. 77–114.
[22] A., Dawar, Generalized quantifiers and logical reducibilities, Journal of Logic and Computation, vol. 5 (1995), pp. 213–226.
[23] A., Dawar, M., Grohe, and S., Kreutzer, Locally excluding a minor, Proc. of the 22nd IEEE Symp. on Logic in Computer Science, 2007, pp. 270–279.
[24] A., Dawar, M., Grohe, S., Kreutzer, and N., Schweikardt, Approximation schemes for first-order definable optimisation problems, Proc. of the 21st IEEE Symp. on Logic in Computer Science, 2006, pp. 411–420.
[25] A., Dawar, S., Lindell, and S., Weinstein, Infinitary logic and inductive definability over finite structures, Information and Computation, vol. 119 (1995), pp. 160–175.
[26] E. D., Demaine, F. V., Fomin,M. T., Hajiaghayi, and D. M., Thilikos, Subexponential parameterized algorithms on bounded-genus graphs and h-minorfree graphs, Journal of the ACM, vol. 52 (2005), no. 6, pp. 866–893.
[27] E.D., Demaine, M., Hajiaghayi, and K., Kawarabayashi, Approximation algorithms via structural results for apex-minor-free graphs, Proc. of the 36th International Colloquium on Automata, Languages and Programming, Part I(S., Albers, A., Marchetti-Spaccamela, Y., Matias, S.E., Nikoletseas, and W., Thomas, editors), Lecture Notes in Computer Science, vol. 5555, Springer- Verlag, 2009, pp. 316–327.
[28] E.D., Demaine, M. T., Hajiaghayi, and K., Kawarabayashi, Algorithmic graph minor theory: Decomposition, approximation, and coloring., Proc. of the 45th Annual IEEE Symp. on Foundations of Computer Science, 2005, pp. 637–646.
[29] R., Diestel, Graph Theory, 3rd ed., Springer-Verlag, 2005.
[30] H.-D., Ebbinghaus, Extended logics: The general framework, Model- Theoretic Logics (J., Barwise and S., Feferman, editors), Springer-Verlag, 1985, pp. 25–76.
[31] H.-D., Ebbinghaus and J., Flum, Finite Model Theory, 2nd ed., Springer- Verlag, 1999.
[32] H.-D., Ebbinghaus, J., Flum, and W., Thomas, Mathematical Logic, 2nd ed., Springer-Verlag, 1994.
[33] Z., Endemann,, 2012, Personal communication.
[34] R., Fagin, Generalized first-order spectra and polynomial-time recognizable sets, Complexity of Computation, SIAM-AMS Proc., Vol. 7 (R.M. Karp, editor), 1974, pp. 43–73.
[35] I. S., Filotti and J. N., Mayer, A polynomial-time algorithm for determining the isomorphism of graphs of fixed genus, Proc. of the 12th ACM Symp. on Theory of Computing, 1980, pp. 236–243.
[36] L. S., Filotti, G. L., Miller, and J., Reif, On determining the genus of a graph in O(vO(g)) steps, Proc. of the 11th ACMSymp. on Theory of Computing, 1979, pp. 27–37.
[37] J., Flum and M., Grohe, On fixed-point logic with counting, The Journal of Symbolic Logic, vol. 65 (2000), no. 2, pp. 777–787.
[38] E., Grädel, Finite model theory and descriptive complexity, E., Grädel, P.G., Kolaitis, L., Libkin, M., Marx, J., Spencer, M.Y., Vardi, Y., Venema, and S., Weinstein, Finite Model Theory and Its Applications, Springer-Verlag, 2007, pp. 12–230.
[39] E., Grädel, P., G.|Kolaitis, L., Libkin, M., Marx, J., Spencer, M., Y.|Vardi, Y., Venema, and S., Weinstein, Finite Model Theory and Its Applications, Springer-Verlag, 2007.
[40] E., Grädel and M., Otto, Inductive definability with counting on finite structures, Computer Science Logic, 6th Workshop, CSL '92, San Miniato 1992, Selected Papers(E., Börger, G., Jäger, H. Kleine, Büning, S., Martini, and M.M., Richter, editors), Lecture Notes in Computer Science, vol. 702, Springer-Verlag, 1993, pp. 231–247.
[41] M., Grohe, Arity hierarchies, Annals of Pure and Applied Logic, vol. 82 (1996), no. 2, pp. 103–163.
[42] M., Grohe, Fixed-point logics on planar graphs, Proc. of the 13th IEEE Symp. on Logic in Computer Science, 1998, pp. 6–15.
[43] M., Grohe, Isomorphism testing for embeddable graphs through definability, Proc. of the 32nd ACM Symp. on Theory of Computing, 2000, pp. 63–72.
[44] M., Grohe, Local tree-width, excluded minors, and approximation algorithms, Combinatorica, vol. 23 (2003), no. 4, pp. 613–632.
[45] M., Grohe, Definable tree decompositions, Proc. of the 23rd IEEE Symp. on Logic in Computer Science, 2008, pp. 406–417.
[46] M., Grohe, Fixed-point definability and polynomial time on chordal graphs and line graphs, Fields of Logic and Computation: Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday (A., Blass, N., Dershowitz, and W., Reisig, editors), Lecture Notes in Computer Science, vol. 6300, Springer- Verlag, 2010, pp. 328–353.
[47] M., Grohe, Fixed-point definability and polynomial time on graphs with excluded minors, Proc. of the 25th IEEE Symp. on Logic in Computer Science, 2010, pp. 179–188.
[48] M., Grohe, From polynomial time queries to graph structure theory, Communications of the ACM, vol. 54 (2011), no. 6, pp. 104–112.
[49] M., Grohe, Fixed-point definability and polynomial time on graphs with excluded minors, Journal of the ACM, vol. 59 (2012), no. 5.
[50] M., Grohe, Quasi-4-connected components, Proc. of the 43rd International Colloquium on Automata, Languages and Programming (Track A)(I., Chatzigiannakis, M., Mitzenmacher, Y., Rabani, and D., Sangiorgi, editors), LIPIcs, vol. 55, SchlossDagstuhl –Leibniz-Zentrum f ür Informatik, 2016, pp. 8:1–8:13.
[51] M., Grohe, Tangled up in blue (a survey on connectivity, decompositions, and tangles), ArXiv (CoRR), vol. arXiv:1605.06704 [cs.DM] (2016).
[52] M., Grohe, B., Grußien, A., Hernich, and B., Laubner, L-recursion and a new logic for logarithmic space, Logical Methods in Computer Science, vol. 9 (2012).
[53] M., Grohe and J., Mariño, Definability and descriptive complexity on databases of bounded tree-width, Proc. of the 7th International Conference on Database Theory (C., Beeri and P., Buneman, editors), Lecture Notes in Computer Science, vol. 1540, Springer-Verlag, 1999, pp. 70–82.
[54] M., Grohe and D., Marx, Structure theorem and isomorphism test for graphs with excluded topological subgraphs, SIAM Journal on Computing, vol. 44 (2015), no. 1, pp. 114–159.
[55] M., Grohe and M., Otto, Pebble games and linear equations, Proc. of the 26th International Workshop on Computer Science Logic(P., Cégielski and A., Durand, editors), Leibniz International Proc. in Informatics (LIPIcs), vol. 16, 2012, pp. 289–304.
[56] M., Grohe and P., Schweitzer, Isomorphism testing for graphs of bounded rank width, Proc. of the 55th Annual IEEE Symp. on Foundations of Computer Science, 2015, pp. 1010–1029.
[57] J. L., Gross and T.W., Tucker, Topological Graph Theory,Wiley, 1987.
[58] B., Grussien, Isoperimetric inequalities on the hexagonal grid, ArXiv, vol. arXiv:1201.0697 [math.CO] (2012).
[59] Y., Gurevich, Toward logic tailored for computational complexity, Computation and Proof Theory (M. M., Richter, E., Börger, W., Oberschelp, B., Schinzel, and W., Thomas, editors), Lecture Notes in Mathematics, vol. 1104, Springer-Verlag, 1984, pp. 175–216.
[60] Y., Gurevich, Logic and the challenge of computer science, Current Trends in Theoretical Computer Science (E., Börger, editor), Computer Science Press, 1988, pp. 1–57.
[61] Y., Gurevich and S., Shelah, Fixed point extensions of first-order logic, Annals of Pure and Applied Logic, vol. 32 (1986), pp. 265–280.
[62] R., Halin, S-Functions for graphs, Journal of Geometry, vol. 8 (1976), pp. 171–186.
[63] L., Hella, Logical hierarchies in PTIME, Information and Computation, vol. 129 (1996), pp. 1–19.
[64] L., Hella, Ph. G., Kolaitis, and K., Luosto, Almost everywhere equivalence of logics in finite model theory, The Bulletin of Symbolic Logic, vol. 2 (1996), pp. 422–443.
[65] W., Hildesheimer, Ich trage eine Eule nach Athen, Lieblose Legenden, Suhrkamp Verlag, 1962.
[66] J. E., Hopcroft and R., Tarjan, Isomorphism of planar graphs (working paper), Complexity of Computer Computations (R. E., Miller and J.W., Thatcher, editors), Plenum Press, 1972.
[67] J. E., Hopcroft and J. K., Wong, Linear time algorithm for isomorphism of planar graphs, Proc. of the 6th ACM Symp. on Theory of Computing, 1974, pp. 172–184.
[68] J.E., Hopcroft, An n log n algorithm for minimizing states in a finite automaton, Theory of Machines and Computations (Z., Kohavi and A., Paz, editors), Academic Press, 1971, pp. 189–196.
[69] N., Immerman, Number of quantifiers is better than number of tape cells, Journal of Computer and System Sciences, vol. 22 (1981), pp. 384–406.
[70] N., Immerman, Relational queries computable in polynomial time (extended abstract), Proc. of the 14thACMSymp. on Theory of Computing, 1982, pp. 147–152.
[71] N., Immerman, Upper and lower bounds for first-order expressibility, Journal of Computer and System Sciences, vol. 25 (1982), pp. 76–98.
[72] N., Immerman, Relational queries computable in polynomial time, Information and Control, vol. 68 (1986), pp. 86–104.
[73] N., Immerman, Expressibility as a complexity measure: results and directions, Proc. of the 2nd IEEE Symp. on Structure in Complexity Theory, 1987, pp. 194–202.
[74] N., Immerman, Languages that capture complexity classes, SIAM Journal on Computing, vol. 16 (1987), pp. 760–778.
[75] N., Immerman, Descriptive Complexity, Springer-Verlag, 1999.
[76] N., Immerman and E., Lander, Describing graphs: A first-order approach to graph canonization, Complexity Theory Retrospective (A., Selman, editor), Springer-Verlag, 1990, pp. 59–81.
[77] R. M., Karp, Reducibilities among combinatorial problems, Complexity of Computer Computations (R.E., Miller and J.W., Thatcher, editors), Plenum Press, New York, 1972, pp. 85–103.
[78] Ph. G., Kolaitis and M. Y., Vardi, Infinitary logic and 0-1 laws, Information and Computation, vol. 98 (1992), pp. 258–294.
[79] Ph. G., Kolaitis and M. Y., Vardi, On the expressive power of datalog: tools and a case study, Journal of Computer and System Sciences, vol. 51 (1995), no. 1, pp. 110–134.
[80] Ph. G., Kolaitis and M. Y., Vardi, On the expressive power of variable-confined logics, Proc. of the 26th IEEE Symp. on Logic in Computer Science, 1996, pp. 348–359.
[81] S., Kreutzer, Expressive equivalence of least and inflationary fixedpoint logic, Proc. of the 17th IEEE Symp. on Logic in Computer Science, 2002, pp. 403–413.
[82] K., Kuratowski, Sur le problème des courbes gauches en topologie, Fundamenta Mathematicae, vol. 15 (1930), pp. 271–283.
[83] B., Laubner, Capturing polynomial time on interval graphs, Proc. of the 25th IEEE Symp. on Logic in Computer Science, 2010, pp. 199–208.
[84] B., Laubner, The Structure of Graphs and New Logics for the Characterization of Polynomial Time, Ph.D. thesis, Humboldt-Universität zu Berlin, 2011.
[85] H. I., Levine, Homotopic curves on surfaces, Proc. of the American Mathematical Society, vol. 14 (1963), pp. 986–990.
[86] L., Libkin, Elements of Finite Model Theory, Springer-Verlag, 2004.
[87] E. M., Luks, Isomorphism of graphs of bounded valance can be tested in polynomial time, Journal of Computer and System Sciences, vol. 25 (1982), pp. 42–65.
[88] P., Malkin, Sherali–Adams relaxations of graph isomorphism polytopes, Discrete Optimization, vol. 12 (2014), pp. 73–97.
[89] G. L., Miller, Isomorphism testing for graphs of bounded genus, Proc. of the 12th ACM Symp. on Theory of Computing, 1980, pp. 225–235.
[90] G. L., Miller, Isomorphism of graphs which are pairwise k-separable, Information and Control, vol. 56 (1983), pp. 21–33.
[91] B., Mohar, A linear time algorithm for embedding graphs in an arbitrary surface, SIAM Journal on Discrete Mathematics, vol. 12 (1999), pp. 6–26.
[92] B., Mohar and C., Thomassen, Graphs on Surfaces, Johns Hopkins University Press, 2001.
[93] D., Neuen, Graph isomorphism for unit square graphs, Proc. of the 24th Annual European Symp. on Algorithms (ESA 2016) (P., Sankowski and Ch.D., Zaroliagis, editors), LIPIcs, vol. 57, Schloss Dagstuhl –Leibniz-Zentrum f ür Informatik, 2016, pp. 70:1–70:17.
[94] M., Otto, Bounded Variable Logics and Counting –A Study in Finite Models, Lecture Notes in Logic, vol. 9, Springer-Verlag, 1997.
[95] M., Otto, Capturing bisimulation-invariant Ptime., Proc. of the 4th International Symp. on Logical Foundations of Computer Science (S.I., Adian and A., Nerode, editors), Lecture Notes in Computer Science, vol. 1234, Springer-Verlag, 1997, pp. 294–305.
[96] S.-I., Oum and P. D., Seymour, Approximating clique-width and branchwidth, Journal of Combinatorial Theory, Series B, vol. 96 (2006), pp. 514–528.
[97] R., Paige and R. E., Tarjan, Three partition refinement algorithms, SIAM Journal on Computing, vol. 16 (1987), no. 6, pp. 973–989.
[98] L., Perkovic and B., Reed, An improved algorithm for finding tree decompositions of small width, International Journal of Foundations of Computer Science, vol. 11 (2000), no. 3, pp. 365–371.
[99] O., Pikhurko and O., Verbitsky, Logical complexity of graphs: a survey, Model Theoretic Methods in Finite Combinatorics (M., Grohe and J. A., Makowsky, editors), Contemporary Mathematics, vol. 558, American Mathematical Society, 2011, pp. 129–180.
[100] B., Poizat, Deux ou trois choses que je sais de Ln, The Journal of Symbolic Logic, vol. 47 (1982), pp. 641–658.
[101] I. N., Ponomarenko, The isomorphism problem for classes of graphs that are invariant with respect to contraction, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), vol. 174 (1988), no. Teor. Slozhn. Vychisl. 3, pp. 147–177, 182, In Russian.
[102] J., Redies, Defining PTIME Problems on Planar Graphs with few Variables, Master's thesis, Department of Compter Science, RWTH Aachen University, 2014.
[103] B., Reed, Finding approximate separators an computing tree-width quickly, Proc. of the 24th ACMSymp. on Theory of Computing, 1992, pp. 221–228.
[104] B., Reed, Tree width and tangles: A new connectivity measure and some applications, Surveys in Combinatorics (R. A., Bailey, editor), LMS Lecture Note Series, vol. 241, Cambridge University Press, 1997, pp. 87–162.
[105] N., Robertson and P. D., Seymour, Graph minors I–XXIII, Journal of Combinatorial Theory, Series B 1982–2012.
[106] N., Robertson and P. D., Seymour, Graph minors II. Algorithmic aspects of tree-width, Journal of Algorithms, vol. 7 (1986), pp. 309–322.
[107] N., Robertson and P. D., Seymour, Graph minors V. Excluding a planar graph, Journal of Combinatorial Theory, Series B, vol. 41 (1986), pp. 92–114.
[108] N., Robertson and P. D., Seymour, Graph minors IX. Disjoint crossed paths, Journal of Combinatorial Theory, Series B, vol. 49 (1990), pp. 40–77.
[109] N., Robertson and P. D., Seymour, Graph minors X. Obstructions to tree-decomposition, Journal of Combinatorial Theory, Series B, vol. 52 (1991), pp. 153–190.
[110] N., Robertson and P. D., Seymour, Graph minors XIII. The disjoint paths problem, Journal of Combinatorial Theory, Series B, vol. 63 (1995), pp. 65–110.
[111] N., Robertson and P. D., Seymour, Graph minors XVI. Excluding a non-planar graph, Journal of Combinatorial Theory, Series B, vol. 77 (1999), pp. 1–27.
[112] N., Robertson, P. D., Seymour, and R., Thomas, Linkless embeddings of graphs in 3-space, Bulletin of the AMS, vol. 28 (1993), pp. 84–89.
[113] N., Robertson and P.D., Seymour, Graph minors XX. Wagner's conjecture, Journal of Combinatorial Theory, Series B, vol. 92 (2004), pp. 325–357.
[114] N., Robertson and R., Vitray, Representativity of surface embeddings, Paths, Flows and VLSI-Layout (B., Korte, L., Lovász, H.J., Pr ömel, and A., Schrijver, editors), Springer-Verlag, 1990, pp. 293–328.
[115] U., Schöning, Graph isomorphism is in the low hierarchy, Journal of Computer and System Sciences, vol. 37 (1988), pp. 312–323.
[116] P., Schweitzer, Towards an isomorphism dichotomy for hereditary graph classes, Proc. of the 32nd International Symp. on Theoretical Aspects of Computer Science (E. W., Mayr and N., Ollinger, editors), LIPIcs, vol. 30, Schloss Dagstuhl –Leibniz-Zentrum f ür Informatik, 2015, pp. 689–702.
[117] D., Seese, Tree-partite graphs and the complexity of algorithms, Technical report, Akademie der Wissenschaften der DDR, Karl Weierstrass Institut f ür Mathematik, 1986.
[118] E., Selman, On fractional isomorphisms, 2013, Diplomarbeit at the Department of Mathematics, Humboldt-Universität zu Berlin.
[119] H. D., Sherali and W. P., Adams, A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems, SIAM Journal on Discrete Mathematics, vol. 3 (1990), no. 3, pp. 411–430.
[120] C., Thomassen, The graph genus problem is NP-complete, Journal of Algorithms, vol. 10 (1988), pp. 458–576.
[121] C., Thomassen, The Jordan–Schönflies Theorem and the classification of surfaces, American Mathematical Monthly, vol. 99 (1992), pp. 116–130.
[122] G., Tinhofer, Anote on compact graphs, DiscreteApplied Mathematics, vol. 30 (1991), pp. 253–264.
[123] J., Torán, On the hardness of graph isomorphism, SIAM Journal on Computing, vol. 33 (2004), no. 5, pp. 1093–1108.
[124] R., Uehara, Simple geometrical intersection graphs, Proc. of the Second International Workshop on Algorithms and Computation, Lecture Notes in Computer Science, vol. 4921, Springer-Verlag, 2008, pp. 25–33.
[125] M. Y., Vardi, The complexity of relational query languages, Proc. of the 14th ACM Symp. on Theory of Computing, 1982, pp. 137–146.
[126] K., Wagner, Über eine Eigenschaft der ebenen Komplexe, Mathematische Annalen, vol. 114 (1937), pp. 570–590.
[127] K., Wagner, Beweis einer Abschwächung der Hadwiger-Vermutung, Mathematische Annalen, vol. 153 (1964), pp. 139–141.
[128] H., Whitney, Congruent graphs and the connectivity of graphs, American Journal of Mathematics, vol. 54 (1932), pp. 150–168.
