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Decomposing Berge graphs
, 2006
"... A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well understo ..."
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A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well
Recognizing Berge graphs
 COMBINATORICA
, 2005
"... A graph is Berge if no induced subgraph of G is an odd cycle of length at least ve or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(V(G)9). This is independent of the recent proof of the strong perfect graph conjecture. ..."
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Cited by 70 (10 self)
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A graph is Berge if no induced subgraph of G is an odd cycle of length at least ve or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(V(G)9). This is independent of the recent proof of the strong perfect graph conjecture.
Chairfree Berge Graphs are Perfect
 GRAPHS COMBIN
, 1996
"... A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge's Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd, eb}. We prove ..."
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Cited by 5 (0 self)
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A graph G is called Berge if neither G nor its complement contains a chordless cycle with an odd number of nodes. The famous Berge's Strong Perfect Graph Conjecture asserts that every Berge graph is perfect. A chair is a graph with nodes {a, b, c, d, e} and edges {ab, bc, cd, eb}. We prove
Algorithms for square3PC(·, ·)free Berge graphs
, 2006
"... We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and squarefree Berge gr ..."
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Cited by 8 (6 self)
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We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This class generalizes clawfree Berge graphs and squarefree Berge
Triangulated neighbourhoods in C_4free Berge graphs
, 1999
"... We call a Tvertex of a graph G = (V; E) a vertex z whose neighbourhood N(z) in G induces a triangulated graph, and we show that every C4 free Berge graph either is a clique or contains at least two nonadjacent Tvertices. An easy consequence of this result is that every C4 free Berge graph admit ..."
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Cited by 1 (0 self)
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We call a Tvertex of a graph G = (V; E) a vertex z whose neighbourhood N(z) in G induces a triangulated graph, and we show that every C4 free Berge graph either is a clique or contains at least two nonadjacent Tvertices. An easy consequence of this result is that every C4 free Berge graph
Transitive orientations in bullreducible Berge graphs
, 2008
"... A bull is a graph with five vertices r, y, x, z, s and five edges ry, yx, yz, xz, zs. A graph G is bullreducible if no vertex of G lies in two bulls. We prove that every bullreducible Berge graph G that contains no antihole is weakly chordal, or has a homogeneous set, or is transitively orientable ..."
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A bull is a graph with five vertices r, y, x, z, s and five edges ry, yx, yz, xz, zs. A graph G is bullreducible if no vertex of G lies in two bulls. We prove that every bullreducible Berge graph G that contains no antihole is weakly chordal, or has a homogeneous set, or is transitively
Loose vertices in C_4free Berge graphs
, 1999
"... Following [8] we call a loose vertex a vertex whose neighbourhood induces a P4 free graph, and we show that every C4 free Berge graph G which is not a clique either is breakable (i.e. G or G has a starcutset) or contains at least two nonadjacent loose vertices. Consequently, every minimal imper ..."
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Following [8] we call a loose vertex a vertex whose neighbourhood induces a P4 free graph, and we show that every C4 free Berge graph G which is not a clique either is breakable (i.e. G or G has a starcutset) or contains at least two nonadjacent loose vertices. Consequently, every minimal
Decomposing Berge graphs containing no proper wheels, stretchers or their complements
, 2003
"... In this paper we show that, if G is a Berge graph such that neither G nor its complement G contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph (a bipartite graph, a line graph of a bipartite graph or the complement of such graphs) or it has ..."
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Cited by 6 (2 self)
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In this paper we show that, if G is a Berge graph such that neither G nor its complement G contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph (a bipartite graph, a line graph of a bipartite graph or the complement of such graphs
Results 1  10
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