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On bperfect chordal graphs
, 2007
"... The bchromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the bchromatic number is eq ..."
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Cited by 4 (1 self)
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The bchromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the bchromatic number
Perfect graphs and graphical modeling
 APPEARS IN TRACTABILITY, CAMBRIDGE UNIVERSITY PRESS
, 2012
"... Tractability is the study of computational tasks with the goal of identifying which problem classes are tractable or, in other words, efficiently solvable. The class of tractable problems is traditionally assumed to be solvable in polynomial time by a deterministic Turing machine and is denoted by P ..."
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. Problems such as maximum stable set, the traveling salesman problem and graph coloring are known to be NPhard (at least as hard as the hardest problems in NP). It is, therefore,
SET COLORINGS IN PERFECT GRAPHS
, 2009
"... Abstract. For a nontrivial connected graph G, let c: V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v ∈ V (G), the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6 = NC(v) fo ..."
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Abstract. For a nontrivial connected graph G, let c: V (G) → N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v ∈ V (G), the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) 6 = NC
Perfect Simulation and Stationarity of a Class of Mobility Models
 in IEEE Infocom
, 2005
"... Abstract — We define “random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm calculus to study the model ..."
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Cited by 106 (3 self)
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. For the special case of random waypoint, we provide for the first time a proof and a sufficient and necessary condition of the existence of a stationary regime. Further, we extend its applicability to a broad class of non convex and multisite examples, and provide a readytouse algorithm for perfect simulation
Graph Colorings on Chordal Graphs
"... Since chordal graphs possess an excellent ("perfect") property on ordinary (vertex) coloring, it is interesting to see what would happen on different colorings. In this talk, we define two graph colorings (or labellings) on a simple graph G = (V; E). First, given positive integers m,n, an ..."
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Since chordal graphs possess an excellent ("perfect") property on ordinary (vertex) coloring, it is interesting to see what would happen on different colorings. In this talk, we define two graph colorings (or labellings) on a simple graph G = (V; E). First, given positive integers m
Two Strikes Against Perfect Phylogeny
 PROC. OF 19TH INTERNATIONAL COLLOQUIUM ON AUTOMATA LANGUAGES AND PROGRAMMING
, 1992
"... One of the major efforts in molecular biology is the computation of phylo genies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algor ..."
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Cited by 123 (28 self)
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to be equivalent to the problem of triangulating colored graphs[30]. It has also been shown recently that for a given fixed number of characters the yesinstances have bounded treewidth[45], opening the possibility of applying methodologies for bounded treewidth to the fixedparameter form of the problem. We
Zero Knowledge and the Chromatic Number
 Journal of Computer and System Sciences
, 1996
"... We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number wi ..."
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Cited by 196 (6 self)
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We present a new technique, inspired by zeroknowledge proof systems, for proving lower bounds on approximating the chromatic number of a graph. To illustrate this technique we present simple reductions from max3coloring and max3sat, showing that it is hard to approximate the chromatic number
Characterization of Uniquely Colorable and Perfect Graphs
, 2014
"... This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The main results are 1) Every uniquely kcolorable graph is (k 1)connected. 2) If G is a uniquely kcolorable graph, then (G) ≥ k l. 3) A maximal planar graph G of order 3 or more has chromatic number 3 if and ..."
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This paper studies the concepts of uniquely colorable graphs & Perfect graphs. The main results are 1) Every uniquely kcolorable graph is (k 1)connected. 2) If G is a uniquely kcolorable graph, then (G) ≥ k l. 3) A maximal planar graph G of order 3 or more has chromatic number 3
Perfect Graphs and Vertex Coloring Problem
, 2006
"... The graph is perfect, if in all its induced subgraphs the size of the largest clique is equal to the chromatic number.In 1960 Berge formulated two conjectures about perfct graphs one stronger than the other, the weak perfect conjecture was proved in 1972 by Lovasz and the strong perfect onjecture w ..."
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was proved in 2003 by Chudnovsky and al.The problem to determine an optimal coloring of a graph is NPcomplete in general case.Grötschell and al developed polynomial algorithm to solve this problem for the whole of the perfect graphs. Indeed their algorithms are not practically efficient. Thus, the search
The Complexity of Coloring Games on Perfect Graphs
, 1991
"... In this paper we consider the following type of game: two players must color the vertices of a given graph G = (V, E), in a predescribed order, such that no two adjacent vertices are colored with the same color. In one variant, the first player which is unable to move loses the game. In areother ..."
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Cited by 1 (0 self)
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In this paper we consider the following type of game: two players must color the vertices of a given graph G = (V, E), in a predescribed order, such that no two adjacent vertices are colored with the same color. In one variant, the first player which is unable to move loses the game. In areother
Results 11  20
of
1,393