The Edge-Closure of a Claw-Free Graph is the Line Graph of a Multigraph

Abstract

Ryjáček introduced a closure concept in claw-free graphs based on local completion at a locally connected vertex. He showed that the closure of a graph is the line graph of a triangle-free graph. Broušek and Holub gave an analogous closure concept of claw-free graphs, called the edge-closure, based on local completion at a locally connected edge. In this paper, it is shown that the edge-closure is the line graph of a multigraph.