Mathematics and Natural Sciences
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. (C) 2009 Elsevier B.V. All rights reserved.
Discrete Applied Mathematics
(2009). The Binding Number of a Graph and Its Cliques. Discrete Applied Mathematics, 157(15), 3336-3340.
Available at: https://aquila.usm.edu/fac_pubs/1149