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arXiv · 2203.04250

Edge Intersection Graphs of Paths on a Triangular Grid

Vitor T. F. de Luca·María Pía Mazzoleni·Fabiano S. Oliveira·Tanilson D. Santos·Jayme L. Szwarcfiter
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Abstract

We introduce a new class of intersection graphs, the edge intersection graphs of paths on a triangular grid, called EPGt graphs. We show similarities and differences from this new class to the well-known class of EPG graphs. A turn of a path at a grid point is called a bend. An EPGt representation in which every path has at most $k$ bends is called a B$_k$-EPGt representation and the corresponding graphs are called B$_k$-EPGt graphs. We provide examples of B$_{2}$-EPG graphs that are B$_{1}$-EPGt. We characterize the representation of cliques with three vertices and chordless 4-cycles in B$_{1}$-EPGt representations. We also prove that B$_{1}$-EPGt graphs have Strong Helly number $3$. Furthermore, we prove that B$_{1}$-EPGt graphs are $7$-clique colorable.

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Vitor T. F. de Luca, María Pía Mazzoleni, Fabiano S. Oliveira, Tanilson D. Santos, Jayme L. Szwarcfiter. 2022-03-08. Edge Intersection Graphs of Paths on a Triangular Grid. https://arxiv.org/abs/2203.04250

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