Subgraphs in vertex neighborhoods of Kr‐free graphs
Jørgen Bang‐Jensen, Stephan Brandt · Journal of Graph Theory · 2004
Abstract In a Kr‐free graph, the neighborhood of every vertex induces a Kr − 1‐free subgraph. The Kr‐free graphs with the converse property that every induced Kr − 1‐free subgraph is contained in the neighborhood of a vertex are characterized, based on the characterization in the case r − 3 due to Pach [ 8 ]. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 29–38, 2004