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Graphs and k-Societies

Published online by Cambridge University Press:  20 November 2018

Pavol Hell  and
Jaroslav Nešetřil
Pavol Hell
Affiliation:
Mcmaster University, Hamilton, Ontario
Jaroslav Nešetřil
Affiliation:
Mcmaster University, Hamilton, Ontario
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Extract

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A graph G is a couple (X, R) where X is a set, R ⊂ X × X. If G is an undirected graph without loops (R a symmetric irreflexive relation), we can interpret G as a couple (X, R), where R is a set of two-element subsets of X, i.e. . This interpretation is generalized in the notion of society.

A society is a couple (X, R), where ; a k-society is a society (X, R) with |A| = k for each A ∊ R.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 3 , September 1970 , pp. 375 - 381
Copyright
Copyright © Canadian Mathematical Society 1970

Footnotes

(2)

Part of this paper was written while the authors were supported by the National Research Council of Canada.

(1)

Sometimes, instead of society (k-society), the words set-system (uniform set-system) or hypergraph are used.

References

1. Berge, C., Theory of graphs and their applications, J. Wiley, New York, 1962.Google Scholar
2. Hedrlin, Z., Pultr, A.: Symetrie relations (undirected graphs) with given semigroup, Mhf. fiir Math. 68 (1965), 318-322.Google Scholar
3. Mendelsohn, E., Sips, products, and graphs with given semigroup, (to appear).Google Scholar
4. Pultr, A., On selecting ofmorphisms, CMUC (1), 8 (1967), 53-83.Google Scholar
5. Vopěnka, P., Pultr, A., Hedrlin, Z., A rigid relation exists on any set CMUC (2), 6 (1965), 149-155.Google Scholar