Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-10T09:49:15.520Z Has data issue: false hasContentIssue false
  • English
  • Français

Sum-free sets, coloured graphs and designs

Published online by Cambridge University Press:  09 April 2009

Anne Penfold Street  and
W. D. Wallis
Anne Penfold Street
Affiliation:
Department of MathematicsUniversity of Queensland.
W. D. Wallis
Affiliation:
Department of MathematicsUniversity of Newcastle.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Sum-free sets may be used to colour the edges of a complete graph in such a way as to avoid monochromatic triangles. We discuss the automorphism groups of such graphs. Embedding of colourings is considered. Finally we illustrate a way of constructing colourings using block designs.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1976 , pp. 35 - 53
Copyright
Copyright © Australian Mathematical Society 1976

References

Chung, Fan Rong K. (1973), ‘On the Ramsey numbers N(3,3, …, 3;2)’, Discrete Math. 5, 317–321.CrossRefGoogle Scholar
Fan, Chung (1974), ‘On triangular and cyclic Ramsey numbers with k colours’, Graphs and Combinatorics, Proc. of the Capital Conf. on Graph Theory and Combinatorics at the George Washington Univ., 1973. Lecture Notes in Mathematics 406 (ed. Mathematics Bari, A. & Frank, Harary), and pp. 236–242.Google Scholar
Jon, Folkman (1967), ‘Notes on the Ramsey number N(3,3,3,3)’, Manuscript, Rand Corp., Santa Monica.Google Scholar
Greenwood, R. E. and Gleason, A. M. (1955), ‘Combinatorial relations and chromatic graphs’, Canad. J. Math. 7, 1–7.CrossRefGoogle Scholar
Kalbfleisch, J. G. and Stanton, R. G. (1968), ‘On the maximal triangle-free edge-chromatic graphs in three colours’, J. Combinatorial Theory 5, 9–20.CrossRefGoogle Scholar
Wallis, W. D., Anne Penfold Street and Jennifer Seberry Wallis (1972), Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Lecture Notes in Mathematics 292, Springer-Verlag.CrossRefGoogle Scholar
Whitehead, E. G. Jr (1971), ‘Algebraic structure of chromatic graphs associated with the Ramsey number N(3,3,3;2)’, Discrete Math. 1, 113–114.CrossRefGoogle Scholar
Whitehead, E. G. Jr (1973), ‘The Ramsey number N(3,3,3,3;2)’, Discrete Math. 4, 389–396.CrossRefGoogle Scholar
Whitehead, E. G. Jr (1975), ‘Difference sets and sum-free sets in groups of order 16’, Discrete Math. (to appear).Google Scholar