On $B_1$-EPG and EPT graphs

On $B_1$-EPG and EPT graphs

This research contains as a main result the prove 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 pr...

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Hauptverfasser: Alcón, Liliana, Mazzoleni, María Pía, Santos, Tanilson Dias dos
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
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Zusammenfassung:This research contains as a main result the prove 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 of Bipartite graphs.
DOI:10.48550/arxiv.2007.02755