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On Graphs that do not Contain a Thomsen Graph

Published online by Cambridge University Press:  20 November 2018

W. G. Brown*
Affiliation:
University of British Columbia
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A Thomsen graph [2, p. 22] consists of six vertices partitioned into two classes of three each, with every vertex in one class connected to every vertex in the other; it is the graph of the “gas, water, and electricity” problem [1, p. 206]. (All graphs considered in this paper will be undirected, having neither loops nor multiple edges.)

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Berge, C., Théorie des graphes. (Paris, 1958).Google Scholar
2. Coxeter, H. S. M. and Moser, W.O.J., Generators and Relations for Discrete Groups, (Springer Verlag, 1957).Google Scholar
3. Dixkson, L.E., Theory of Numbers, Volume II, (Chelsea Publishing Company, 1952).Google Scholar
4. Erdős, P., Extremal problems in graph theory, in Theory of Graphs and its Applications, edited by Fiedler, M. (Prague-New York-London, 1964).Google Scholar
5. Erdő's, P., On extremal problems of graphs and generalized graphs, Israel J. Math. 2, (1964), 183-190.CrossRefGoogle Scholar
6. Hardy, G.H. and Wright, E.M., An introduction to the theory of numbers (Fourth Edition), (Oxford, 1960).Google Scholar
7. Kőväri, T., Sós, V.T., Turän, P., On a problem of K. Zarankiewicz. Coll. Math. 3, (1955), 50-57.CrossRefGoogle Scholar
8. Znäm, š., Two improvements of a result concerning a problem of K. Zarankiewicz, Colloq. Math. 13, (1965), 255-258.CrossRefGoogle Scholar
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On Graphs that do not Contain a Thomsen Graph
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