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Coloring Meyniel graphs in linear time
 Cahiers Leibniz 105 (2004), accepted in Information Processing Letters, available on http://hal.ccsd.cnrs.fr/ccsd00001574
"... A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. We present a lineartime algorithm that colors optimally the vertices of a Meyniel graph and finds a clique of maximum size. 1 ..."
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A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. We present a lineartime algorithm that colors optimally the vertices of a Meyniel graph and finds a clique of maximum size. 1
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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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 admits a Telimination scheme, i.e. an ordering [v1 ; v2 ; : : : ; vn ] of its vertices such that v i is a Tvertex in the subgraph induced by v i ; : : : ; vn in G.
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 imperfect C4 free graph has loose vertices.
Vertex elimination orderings for hereditary graph classes
, 2014
"... AMS Classification: 05C75 We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its pro ..."
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AMS Classification: 05C75 We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before, but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs discovered by Maffray, Trotignon and Vušković. 1