AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and the size of the largest complete subgraph. Our results extends a theorem due to Brooks
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...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
AbstractFour bounds for the chromatic number have been calculated for several graphs. The same metho...
AbstractWe show that for sufficiently large Δ, any graph with maximum degree at most Δ and no clique...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r ver...
AbstractWe consider the subchromatic number χS(G) of graph G, which is the minimum order of all part...
AbstractIt is proved that for every k⩾4 there is a Δ(k) such that for every g there is a graph G wit...
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...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractLet G be a simple graph, let Δ(G) denote the maximum degree of its vertices, and let χ(G) de...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
AbstractFour bounds for the chromatic number have been calculated for several graphs. The same metho...
AbstractWe show that for sufficiently large Δ, any graph with maximum degree at most Δ and no clique...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r ver...
AbstractWe consider the subchromatic number χS(G) of graph G, which is the minimum order of all part...
AbstractIt is proved that for every k⩾4 there is a Δ(k) such that for every g there is a graph G wit...
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...
Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has ...
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