AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chromatic number of a triangle-free graph with m>1 edges is at most c1m1/3/(logm)2/3 and at least c2m1/3/(logm)2/3. This is deduced from results of Ajtai, Komlós, Szemerédi, Kim and Johansson, and settles a problem of Erdős
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g w...
Abstract. In the 1970s Erdős asked whether the chromatic number of in-tersection graphs of line seg...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
The problem of determining the chromatic number of H-free graphs has been well studied, with particu...
The problem of determining the chromatic number of H-free graphs has been well studied, with particu...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
The chromatic threshold of a class of graphs is the value θ such that any graph in this class with a...
AbstractThe relation of chromatic aspects and the existence of certain induced subgraphs of a triang...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
AbstractV.G. Vizing has shown that the edge-chromatic number of any graph with maximum vertex-degree...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g w...
Abstract. In the 1970s Erdős asked whether the chromatic number of in-tersection graphs of line seg...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
The problem of determining the chromatic number of H-free graphs has been well studied, with particu...
The problem of determining the chromatic number of H-free graphs has been well studied, with particu...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
The chromatic threshold of a class of graphs is the value θ such that any graph in this class with a...
AbstractThe relation of chromatic aspects and the existence of certain induced subgraphs of a triang...
The clique chromatic number of a graph is the minimum number of colours needed to colour its vertice...
AbstractV.G. Vizing has shown that the edge-chromatic number of any graph with maximum vertex-degree...
AbstractGrünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for eve...
A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g w...
Abstract. In the 1970s Erdős asked whether the chromatic number of in-tersection graphs of line seg...
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