Recognizing vertex intersection graphs of paths on bounded degree trees
نویسندگان
چکیده
منابع مشابه
On local edge intersection graphs of paths on bounded degree trees
An undirected graph G is called an EPT graph if it is the edge intersection graph of a family of paths in a tree. We call G a local EPT graph if it is the EPT graph of a collection of paths P which all share a common vertex. In this paper, we characterize the local EPT graphs which can be represented in a host tree with maximum degree h.
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We investigate the class of vertex intersection graphs of paths on a grid, and specifically consider the subclasses that are obtained when each path in the representation has at most k bends (turns). We call such a subclass the Bk-VPG graphs, k ≥ 0. In chip manufacturing, circuit layout is modeled as paths (wires) on a grid, where it is natural to constrain the number of bends per wire for reas...
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We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, known as B0-VPG graphs. Recognizing these graphs is an NP-hard problem. In light of this, we focus on their subclasses. In the paper, we describe polynomial time algorithms for recognizing chordal B0-VPG graphs, and for recognizing B0-VPG graphs that have a representation on a grid ...
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We consider lower bounds on the number of spanning trees of connected graphs with degree bounded by d. The question is of interest because such bounds may improve the analysis of the improvement produced by memorisation in the runtime of exponential algorithms. The value of interest is the constant βd such that all connected graphs with degree bound ed by d have at least β d spanning trees wher...
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Two characterizations of intersection graphs of vertex disjoint paths in a tree, one in terms of maximal clique separator and the other in terms of minimal forbidden subgraphs, are presented. A polynomial recognition algorithm for this class is suggested.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.08.004