Note: The binding number of a graph and its cliques

Authors:
Jeremy Lyle;Wayne Goddard
Affiliations:
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS, USA;School of Computing and Department of Mathematical Sciences, Clemson University, Clemson, SC, USA
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 4
Cited 0

A note on maximal triangle-free graphs

Journal of Graph Theory
Triangles and neighbourhoods of independent sets in graphs

Journal of Combinatorial Theory Series B
Triangle-Free Graphs with Large Degree

Combinatorics, Probability and Computing
Note: On the Structure of Graphs with Bounded Clique Number

Combinatorica

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Abstract

We consider the binding numbers of K"r-free graphs, and improve the upper bounds on the binding number which force a graph to contain a clique of order r. For the case r=4, we provide a construction for K"4-free graphs which have a larger binding number than the previously known constructions. This leads to a counterexample to a conjecture by Caro regarding the neighborhoods of independent sets.