Biclosure and bistability in a balanced bipartite graph

Abstract

AbstractThe k‐biclosure of a balanced bipartite graph wiht color classes A and B is the graph obtained from G by recursively joining pairs of nonadjacent vertices respectively taken in A and B whose degree sum is at least k, until no such pair remains. A property P defined on all the balanced bipartite graphs of order 2n is k‐bistable if whenever G + ab has property P and dG(b) ≧ k then G itself has property P.We present a synthesis of results involving, for some properties, P, the bistability of P, the k‐biclosure of G, the number of edges and the minimum degree. © 1995 John Wiley & Sons, Inc.