Relationship among <i>B<sub>1</sub></i>-EPG, VPT and EPT graphs classes
نویسندگان
چکیده
منابع مشابه
Clique coloring B1-EPG graphs
We consider the problem of clique coloring, that is, coloring the vertices of a given graph such that no (maximal) clique of size at least two is monocolored. It is known that interval graphs are 2-clique colorable. In this paper we prove that B1-EPG graphs (edge intersection graphs of paths on a grid, where each path has at most one bend) are 4-clique colorable. Moreover, given a B1-EPG repres...
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15 صفحه اولOn Independent Set on B1-EPG Graphs
In this paper we consider the Maximum Independent Set problem (MIS) on B1-EPG graphs. EPG (for Edge intersection graphs of Paths on a Grid) was introduced in [9] as the class of graphs whose vertices can be represented as simple paths on a rectangular grid so that two vertices are adjacent if and only if the corresponding paths share at least one edge of the underlying grid. The restricted clas...
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EPG graphs, introduced by Golumbic et al. in 2009, are edge-intersection graphs of paths on an orthogonal grid. The class Bk-EPG is the subclass of EPG graphs where the path on the grid associated to each vertex has at most k bends. Epstein et al. showed in 2013 that computing a maximum clique in B1-EPG graphs is polynomial. As remarked in [Heldt et al., 2014], when the number of bends is at le...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2023
ISSN: ['1234-3099', '2083-5892']
DOI: https://doi.org/10.7151/dmgt.2408