A bound on the dissociation number

Abstract

AbstractThe dissociation number of a graph is the maximum order of a set of vertices of inducing a subgraph that is of maximum degree at most 1. Computing the dissociation number of a given graph is algorithmically hard even when restricted to subcubic bipartite graphs. For a graph with vertices, edges, components, and induced cycles of length 1 modulo 3, we show . Furthermore, we characterize the extremal graphs in which every two cycles are vertex‐disjoint.