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An upper bound on the size of the largest cliques in a graph
Author(s) -
Billionnet Alain
Publication year - 1981
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190050206
Subject(s) - combinatorics , mathematics , vertex (graph theory) , upper and lower bounds , clique , graph , clique graph , discrete mathematics , line graph , graph power , mathematical analysis
We produce in this paper an upper bound for the number of vertices existing in a clique of maximum cardinal. The proof is based in particular on the existence of a maximum cardinal clique that contains no vertex x such that the neighborhood of x is contained in the neighborhood of another vertex y .