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Enumeration of Bicolourable Graphs

Published online by Cambridge University Press:  20 November 2018

Frank Harary  and
Geert Prins
Frank Harary
Affiliation:
University of Michigan and University College, London and Amsterdam
Geert Prins
Affiliation:
University of Michigan and University College, London and Amsterdam
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In a previous paper (2), one of us has derived a formula for the counting series for bicoloured graphs.2 These are graphs each of whose points has been coloured with exactly one of two colours in such a way that every two adjacent points have different colours.

In this paper we first enumerate bicoloured graphs without isolated points and connected bicoloured graphs. This leads us to corresponding problems for bicolourable graphs. Such a graph has the property that its points can be coloured with two colours so as to obtain a bicoloured graph.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 237 - 248
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Harary, F., The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc, 78 (1955), 445–463.Google Scholar
2. Harary, F., On the number of bicolored graphs, Pacific J. Math., 8 (1958), 743–755.Google Scholar
3. Harary, F., Unsolved problems in the enumeration of graphs, Publ. Math. Inst. Hung. Acad. Sci., 5 (1960), 63–95.Google Scholar
4. Harary, F. and G. Prins, The number of homeomorphically irreducible trees, and other species, Acta Math, 101 (1959), 141–162.Google Scholar
5. Kônig, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936; reprinted New- York, 1950).Google Scholar
6. P, G.ôlya, Kombinatorische Anzahlbestimmungen fur Gruppen, Graphen, und chemische Verbindungen, Acta Math, 68 (1937), 145–254.Google Scholar
7. Riddell, R. J. and Uhlenbeck, G. E., On the theory of the virial development of the equation of state of monoatomic gases, J. Chem. Phys. 21 (1953), 2056–2064.Google Scholar
8. Riordan, J., An introduction to combinatorial analysis (New York, 1958), p. 147.Google Scholar
9. Tutte, W. T., A census of planar triangulations, Can. J. Math. 14 (1962), 21–38.Google Scholar