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A note on maximal triangle‐free graphs
Author(s) -
Goddard Wayne,
Kleitman Daniel J.
Publication year - 1993
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.3190170510
Subject(s) - combinatorics , mathematics , independent set , discrete mathematics , graph , simple graph
We show that a maximal triangle‐free graph on n vertices with minimum degree δ contains an independent set of 3δ − n vertices which have identical neighborhoods. This yields a simple proof that if the binding number of a graph is at least 3/2 then it has a triangle. This was conjectured originally by Woodall. © 1993 John Wiley & Sons, Inc.
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