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Another note on cliques and independent sets
Author(s) -
Galvin Fred
Publication year - 2000
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 - 10.1002/1097-0118(200011)35:3<173::aid-jgt2>3.0.co;2-o
Subject(s) - combinatorics , mathematics , vertex (graph theory) , clique , split graph , graph , discrete mathematics , graph theory , independent set , line graph , pathwidth
Entringer, Goddard, and Henning studied graphs in which every vertex belongs to both an ( m + 1)‐clique and an independent ( n + 1)‐set; they proved that there is such a graph of order p if and only if $p\geq m+n+\sqrt{4mn}$ . We give an alternative and slightly easier proof of this fact, relating it to combinatorial matrix theory. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 173–175, 2000