Geodesic
Relationship among B1-EPG, VPT and EPT graphs classes
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 841-858

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This research contains as a main result the proof that every chordal B_1-EPG graph is simultaneously in the graph classes VPT and EPT. In addition, we describe structures that must be present in any B_1-EPG graph which does not admit a Helly-B_1-EPG representation. In particular, this paper presents some features of non-trivial families of graphs properly contained in Helly-B_1-EPG, namely bipartite, block, cactus and line graphs of bipartite graphs.
Keywords: edge-intersection of paths on a grid, edge-intersection graph of paths in a tree, Helly property, intersection graphs, single bend paths, vertex-intersection graph of paths in a tree 
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Alcón, Liliana; Mazzoleni, María Pía; Dias dos Santos, Tanilson. Relationship among B1-EPG, VPT and EPT graphs classes. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 841-858. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a16/