Abstract:The independence number α(G) and the dissociation number diss(G) of a graph G are the largest orders of induced subgraphs of G of maximum degree at most 0 and at most 1, respectively. We consider possible improvements of the obvious inequality 2α(G) ≥ diss(G). For connected cubic graphs G distinct from K 4 , we show 5α(G) ≥ 3diss(G), and describe the rich and interesting structure of the extremal graphs in detail. For bipartite graphs, and, more generally, triangle-free graphs, we also obtain improvements. For… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.