AbstractReed [B. Reed, ω,Δ and χ, Journal of Graph Theory, 27 (1998) 177–212] conjectured that for any graph G, χ(G)≤⌈Δ(G)+ω(G)+12⌉, where χ(G), ω(G), and Δ(G) respectively denote the chromatic number, the clique number and the maximum degree of G. In this paper, we verify this conjecture for some special classes of graphs which are defined by families of forbidden induced subgraphs
We consider only simple graphs. The graph G1 + G2 consists of vertex disjoint copies of G1 and G2 an...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...
AbstractLet G be a graph of order n with chromatic number χ, maximum degree Δ, clique number ω and i...
A class of graphs is χ-bounded if there is a function such that χ(G)≤f(ω(G)) for every induced subgr...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α...
Brooks ’ Theorem implies that if a graph has ∆ ≥ 3 and and χ> ∆, then ω = ∆+1. Borodin and Kosto...
AbstractBrooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 an...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractGiven a graph G with maximum degree Δ≥3, we prove that the acyclic edge chromatic number a′(...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
AbstractUpper bounds for σ+χ and σχ are proved, where σ is the dominationnumber and χ the chromatic ...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
We consider only simple graphs. The graph G1 + G2 consists of vertex disjoint copies of G1 and G2 an...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...
AbstractLet G be a graph of order n with chromatic number χ, maximum degree Δ, clique number ω and i...
A class of graphs is χ-bounded if there is a function such that χ(G)≤f(ω(G)) for every induced subgr...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
Let G be a graph of order n with clique number ω(G), chromatic number χ(G) and independence number α...
Brooks ’ Theorem implies that if a graph has ∆ ≥ 3 and and χ> ∆, then ω = ∆+1. Borodin and Kosto...
AbstractBrooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 an...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractGiven a graph G with maximum degree Δ≥3, we prove that the acyclic edge chromatic number a′(...
We prove that every graph G with chromatic number χ(G) = ∆(G) − 1 and ∆(G) ≥ 66 contains a clique of...
AbstractUpper bounds for σ+χ and σχ are proved, where σ is the dominationnumber and χ the chromatic ...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
We consider only simple graphs. The graph G1 + G2 consists of vertex disjoint copies of G1 and G2 an...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
Given a simple graph G = (V, E), a subset U of V is called a clique if it induces a complete subgrap...
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