AbstractWe prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic number d+1, then G contains two distinct vertices x,y and a collection of d pairwise edge-disjoint paths between x and y. In particular, the line graph of G satisfies Hajós' conjecture
AbstractA proper vertex coloring of a graph G is linear if the graph induced by the vertices of any ...
International audienceWe give a short proof of the following theorem due to Borodin (1990). Every pl...
The path number p(G) of a graph G is the minimum number of paths needed to partition the edge set of...
AbstractWe prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic...
The {\em disjointness graph} $G=G({\cal S})$ of a set of segments ${\cal S}$ in ${R}^d$, $d\ge 2,$ i...
The classical theorem of Vizing states that every graph of maximum degree d admits an edge-coloring ...
AbstractV.G. Vizing has shown that the edge-chromatic number of any graph with maximum vertex-degree...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractWe propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal....
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
For each n and for each r6n − 3 we obtain the maximum number of edges of a connected graph with n ve...
A graph G is said to have property Pm if it contains no subdivision of Km+1 and no subdivision of K...
For a graph G, let (G) denote its chromatic number and (G) denote the order of the largest clique...
AbstractFor each n and for each r⩽n−3 we obtain the maximum number of edges of a connected graph wit...
AbstractA proper vertex coloring of a graph G is linear if the graph induced by the vertices of any ...
International audienceWe give a short proof of the following theorem due to Borodin (1990). Every pl...
The path number p(G) of a graph G is the minimum number of paths needed to partition the edge set of...
AbstractWe prove that, if a graph G (without multiple edges) has maximum degree d and edge-chromatic...
The {\em disjointness graph} $G=G({\cal S})$ of a set of segments ${\cal S}$ in ${R}^d$, $d\ge 2,$ i...
The classical theorem of Vizing states that every graph of maximum degree d admits an edge-coloring ...
AbstractV.G. Vizing has shown that the edge-chromatic number of any graph with maximum vertex-degree...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractWe propose the following conjecture to generalize results of Pósa and of Corrádi and Hajnal....
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
For each n and for each r6n − 3 we obtain the maximum number of edges of a connected graph with n ve...
A graph G is said to have property Pm if it contains no subdivision of Km+1 and no subdivision of K...
For a graph G, let (G) denote its chromatic number and (G) denote the order of the largest clique...
AbstractFor each n and for each r⩽n−3 we obtain the maximum number of edges of a connected graph wit...
AbstractA proper vertex coloring of a graph G is linear if the graph induced by the vertices of any ...
International audienceWe give a short proof of the following theorem due to Borodin (1990). Every pl...
The path number p(G) of a graph G is the minimum number of paths needed to partition the edge set of...
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