Relationship among B₁-EPG, VPT and EPT graphs classes

Abstract

This research contains as a main result the proof that every chordal B₁-EPG graph is simultaneously in the graph classes VPT and EPT. In addition, we describe structures that must be present in any B₁-EPG graph which does not admit a Helly-B1-EPG representation. In particular, this paper presents some features of non-trivial families of graphs properly contained in Helly-B₁-EPG, namely bipartite, block, cactus and line graphs of bipartite graphs.