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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
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
On stable cutsets in clawfree graphs and planar graphs
, 2008
"... A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1 + 3 vertices. It is NPcomplete to decide whether a line graph (hence a clawfree graph) with maximum degree five or a K4free graph admi ..."
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Cited by 3 (1 self)
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A stable cutset in a connected graph is a stable set whose deletion disconnects the graph. Let K4 and K1,3 (claw) denote the complete (bipartite) graph on 4 and 1 + 3 vertices. It is NPcomplete to decide whether a line graph (hence a clawfree graph) with maximum degree five or a K4free graph
TRACEABILITY IN SMALL CLAWFREE GRAPHS
"... Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1. ..."
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Abstract. We prove that a clawfree, 2connected graph with fewer than 18 vertices is traceable, and we determine all nontraceable, clawfree, 2connected graphs with exactly 18 vertices and a minimal number of edges. This complements a result of Matthews on Hamiltonian graphs. 1.
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds
Planarization and acyclic colorings of subcubic clawfree graphs
"... Abstract. We study methods of planarizing and acyclically coloring clawfree subcubic graphs. We give a polynomialtime algorithm that, given such a graph G, produces an independent set Q of at most n/6 vertices whose removal from G leaves an induced planar subgraph P (in fact, P has treewidth at mo ..."
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Cited by 1 (0 self)
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knowledge, this represents the largest known subclass of subcubic graphs such that an optimal acyclic vertex coloring can be found in polynomialtime. We show that this bound is tight by proving that the problem is NPhard for cubic line graphs (and therefore, clawfree graphs) of maximum degree d ≥ 4
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
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
PACKING 3VERTEX PATHS IN CLAWFREE GRAPHS
, 711
"... A Λfactor of a graph G is a spanning subgraph of G whose every component is a 3vertex path. Let v(G) be the number of vertices of G. A graph is clawfree if it does not have a subgraph isomorphic to K1,3. Our results include the following. Let G be a 3connected clawfree graph, x ∈ V (G), e = xy ∈ ..."
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A Λfactor of a graph G is a spanning subgraph of G whose every component is a 3vertex path. Let v(G) be the number of vertices of G. A graph is clawfree if it does not have a subgraph isomorphic to K1,3. Our results include the following. Let G be a 3connected clawfree graph, x ∈ V (G), e = xy
Results 1  10
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393,100