Obstructions to chordal circular-arc graphs of small independence number
نویسندگان
چکیده
منابع مشابه
Obstructions to chordal circular-arc graphs of small independence number
A blocking quadruple (BQ) is a quadruple of vertices of a graph such that any two vertices of the quadruple either miss (have no neighbours on) some path connecting the remaining two vertices of the quadruple, or are connected by some path missed by the remaining two vertices. This is akin to the notion of asteroidal triple used in the classical characterization of interval graphs by Lekkerkerk...
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Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those metho...
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Matrix partition problems generalize graph colouring and homomorphism problems, and occur frequently in the study of perfect graphs. It is difficult to decide, even for a small matrix M , whether the M partition problem is polynomial time solvable or NP-complete (or possibly neither), and whether M -partitionable graphs can be characterized by a finite set of forbidden induced subgraphs (or per...
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The intention of this note is to motivate the researchers to study Hadwiger’s conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G, and let χ(G) denote its chromatic number. Hadwiger’s conjecture states that η(G) ≥ χ(G) and is one of the most important and difficult open problems in graph theory. From the point of view of researchers who are sceptical of the...
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A k-dimensional box is the cartesian product R1 ×R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. A circular arc graph is a ...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2013
ISSN: 1571-0653
DOI: 10.1016/j.endm.2013.10.012