Powers of hhd-free graphs^∗

^∗First author supported by DAAD and by VW, Project No. 1/69041. second author supported by DFG.

Abstract

The k-the power of a graph G is the graph with the same vertex set as G where two vertices are adjacent iff 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.

Keywords:

• HHD-free graph
• powers of graph
• chordal

C.R. Categories:

• G.2.2

^∗First author supported by DAAD and by VW, Project No. 1/69041. second author supported by DFG.

^∗Corresponding author.

^∗First author supported by DAAD and by VW, Project No. 1/69041. second author supported by DFG.

^∗Corresponding author.

Notes

^∗First author supported by DAAD and by VW, Project No. 1/69041. second author supported by DFG.

^∗Corresponding author.

Additional information

Notes on contributors

Falk Nicolai

b

Andreas Brandstädt

c