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Clawfree Graphs VI. Colouring
, 2011
"... In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can be ..."
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Cited by 4 (0 self)
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In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
The Chromatic Index of a Graph Whose Core has Maximum Degree 2
"... Let G be a graph. The core of G, denoted by G∆, is the subgraph of G induced by the vertices of degree ∆(G), where ∆(G) denotes the maximum degree of G. A kedge coloring of G is a function f: E(G) → L such that L  = k and f(e1) ̸ = f(e2) for all two adjacent edges e1 and e2 of G. The chromatic ..."
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Let G be a graph. The core of G, denoted by G∆, is the subgraph of G induced by the vertices of degree ∆(G), where ∆(G) denotes the maximum degree of G. A kedge coloring of G is a function f: E(G) → L such that L  = k and f(e1) ̸ = f(e2) for all two adjacent edges e1 and e2 of G. The chromatic
Clique minors in clawfree graphs
 J. Combin. Theory Ser. B
"... Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n α. In this paper we prove that this ..."
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Cited by 1 (0 self)
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that this is true for connected clawfree graphs with α ≥ 3. We also show that this result is tight by providing an infinite family of clawfree graphs with α ≥ 3 that do not have a clique minor of size larger than n α
On the choice number of clawfree perfect graphs
 6th International Conference on Graph Theory, Discrete Math
, 2006
"... We show that every 3chromatic clawfree perfect graph is also 3choosable. ..."
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Cited by 1 (0 self)
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We show that every 3chromatic clawfree perfect graph is also 3choosable.
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
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Cited by 12 (1 self)
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In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Minimal ClawFree Graphs
, 2007
"... A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and character ..."
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A graph G is a minimal clawfree graph (m.c.f. graph) if it contains no K1,3 (claw) as an induced subgraph and if, for each edge e of G, G − e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Results 1  10
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355,489