Powers of HHD-free graphs

Abstract

The k-th power of a graph G is the graph with the same vertex set as G where two vertices are adjacent if their distance in G is at most k. In this paper we consider HHD-free graphs, i.e. the graphs where each cycle of length at least five has two chords. We show, that odd powers of HHD-free graphs are again HHD-free, and characterize those HHD-free graphs by forbidden subgraphs for which odd powers are chordal, and even powers are HHD-free or chordal respectively. (orig.)Available from TIB Hannover: RO 1945(315) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman