منابع مشابه
Perfectness of clustered graphs
Given a clustered graph (G,V), that is, a graph G = (V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0-1 matrix M(G,V). Nevertheless, we observe that, given (G,V), it i...
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The clique-transversal number τc(G) of a graph G is the minimum size of a set of vertices meeting all the cliques. The clique-independence number αc(G) of G is the maximum size of a collection of vertex-disjoint cliques. A graph is clique-perfect if these two numbers are equal for every induced subgraph of G. Unlike perfect graphs, the class of clique-perfect graphs is not closed under graph co...
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Given a pair of non-negative integers m and n, S(m,n) denotes a square lattice graph with a vertex set {0, 1, 2, . . . ,m − 1} × {0, 1, 2, . . . , n− 1}, where a pair of two vertices is adjacent if and only if the distance is equal to 1. A triangular lattice graph T (m,n) has a vertex set {(xe1 + ye2) | x ∈ {0, 1, 2, . . . ,m− 1}, y ∈ {0, 1, 2, . . . , n− 1}} where e1 def. = (1, 0), e2 def. = (...
متن کاملCompletely Connected Clustered Graphs
Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the property that not only every cluster but also each complement of a cluster induces a connected subgraph. As a main result, we prove that a completely connected clustered graph is c-planar if and only if the underlying graph is p...
متن کاملMultilayer Drawings of Clustered Graphs
The cluster adjacency graph of a flat clustered graph C(G, T ) is the graph A whose vertices are the clusters in T and whose edges connect clusters containing vertices that are adjacent in G. A multilayer drawing of a clustered graph C consists of a straight-line c-planar drawing of C in which the clusters are drawn as convex regions and of a straight-line planar drawing of A such that each ver...
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2013
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2013.07.006