AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] that for any graph G, the graph’s chromatic number χ(G) is bounded above by ⌈Δ(G)+1+ω(G)2⌉, where Δ(G) and ω(G) are the maximum degree and clique number of G, respectively. In this paper we prove that this bound holds if G is the line graph of a multigraph. The proof yields a polynomial time algorithm that takes a line graph G and produces a colouring that achieves our bound
The colouring number of a graph G, defined as col(G) = 1 + maxH⊆G δ(H), is an upper bound for its c...
AbstractFour bounds for the chromatic number have been calculated for several graphs. The same metho...
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α...
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] ...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
The problem of determining the chromatic index of the arbitrary graph G is known to be NP-complete. ...
AbstractThe chromatic index problem is known to be NP-complete, even for line graphs. In this paper ...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same ...
The colouring number of a graph G, defined as col(G) = 1 + maxH⊆G δ(H), is an upper bound for its c...
AbstractFour bounds for the chromatic number have been calculated for several graphs. The same metho...
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α...
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] ...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
The problem of determining the chromatic index of the arbitrary graph G is known to be NP-complete. ...
AbstractThe chromatic index problem is known to be NP-complete, even for line graphs. In this paper ...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same ...
The colouring number of a graph G, defined as col(G) = 1 + maxH⊆G δ(H), is an upper bound for its c...
AbstractFour bounds for the chromatic number have been calculated for several graphs. The same metho...
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α...
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