Let Gn be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices. Then Gn contains a vertex of degree not exceeding n(3r-7)/(3r-4). The result is essentially best possible. © 1974
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractIn this paper we discuss the existence of lower bounds for the chromatic number of graphs in...
AbstractLet G be any graph, and also let Δ(G), χ(G) and α(G) denote the maximum degree, the chromati...
AbstractLet Gn be a graph of n vertices, having chromatic number r which contains no complete graph ...
AbstractLet Gn be a graph of n vertices, having chromatic number r which contains no complete graph ...
AbstractLet Gr(n) be an r-chromatic graph with n vertices in each colour class. Suppose G = G3(n), a...
summary:In this paper we characterize $k$-chromatic graphs without isolated vertices and connected $...
summary:In this paper we characterize $k$-chromatic graphs without isolated vertices and connected $...
AbstractFor given n, let G be a triangle-free graph of order n with chromatic number at least 4. In ...
summary:In this paper, we show that the maximal number of minimal colourings of a graph with $n$ ver...
summary:In this paper, we show that the maximal number of minimal colourings of a graph with $n$ ver...
AbstractIt is proved that for every k⩾4 there is a Δ(k) such that for every g there is a graph G wit...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
Let Gr(n) be an r-chromatic graph with n vertices in each colour class. Suppose G = G3(n), and δ(G),...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractIn this paper we discuss the existence of lower bounds for the chromatic number of graphs in...
AbstractLet G be any graph, and also let Δ(G), χ(G) and α(G) denote the maximum degree, the chromati...
AbstractLet Gn be a graph of n vertices, having chromatic number r which contains no complete graph ...
AbstractLet Gn be a graph of n vertices, having chromatic number r which contains no complete graph ...
AbstractLet Gr(n) be an r-chromatic graph with n vertices in each colour class. Suppose G = G3(n), a...
summary:In this paper we characterize $k$-chromatic graphs without isolated vertices and connected $...
summary:In this paper we characterize $k$-chromatic graphs without isolated vertices and connected $...
AbstractFor given n, let G be a triangle-free graph of order n with chromatic number at least 4. In ...
summary:In this paper, we show that the maximal number of minimal colourings of a graph with $n$ ver...
summary:In this paper, we show that the maximal number of minimal colourings of a graph with $n$ ver...
AbstractIt is proved that for every k⩾4 there is a Δ(k) such that for every g there is a graph G wit...
AbstractWe give an upper bound on the chromatic number of a graph in terms of its maximum degree and...
Let Gr(n) be an r-chromatic graph with n vertices in each colour class. Suppose G = G3(n), and δ(G),...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
AbstractA lower bound is obtained for the chromatic number X(G) of a graph G in terms of its vertex ...
AbstractIn this paper we discuss the existence of lower bounds for the chromatic number of graphs in...
AbstractLet G be any graph, and also let Δ(G), χ(G) and α(G) denote the maximum degree, the chromati...
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