منابع مشابه
On 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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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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A graph G is called Bk-VPG (resp., Bk-EPG), for some constant k ≥ 0, if it has a string representation on a grid such that each vertex is an orthogonal path with at most k bends and two vertices are adjacent in G if and only if the corresponding strings intersect (resp., the corresponding strings share at least one grid edge). If two adjacent strings of a Bk-VPG graph intersect exactly once, th...
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In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
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For the maximum independent set problem, strong inapproximability bounds for worst-case efficient algorithms exist. We give a deterministic algorithm beating these bounds, with polynomial expected running-time for semi-random graphs: An adversary chooses a graph with n vertices, and then edges are flipped with a probability of ε. Our algorithm guarantees an approximation ratio of O( √ nε) for s...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2020
ISSN: 0166-218X
DOI: 10.1016/j.dam.2019.10.019