AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-free graph with e edges then the chromatic number of G is at most ce1/3(loge)−2/3 for some constant c. In a previous paper, we found an upper bound on the chromatic number of a triangle-free graph of genus g. Using the new result, we slightly improve this bound to cg1/3(logg)−2/3. Both bounds are best possible, up to a constant multiple
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
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...
For every graph G having chromatic number k there is a smallest positive integer i such that every k...
The chromatic number of a triangle-free graph can be arbitrarily large. In this article, we show tha...
In 1967, Erdős asked for the greatest chromatic number, $f(n)$, amongst all $n$-vertex, triangle-fre...
AbstractThe relation of chromatic aspects and the existence of certain induced subgraphs of a triang...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g w...
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
AbstractCombining recent results on colorings and Ramsey theory, we show that if G is a triangle-fre...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
Motivated by a recent conjecture of the first author, we prove that every properly coloured triangle...
AbstractIt is shown that there are two positive constants c1,c2 such that the maximum possible chrom...
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...
For every graph G having chromatic number k there is a smallest positive integer i such that every k...
The chromatic number of a triangle-free graph can be arbitrarily large. In this article, we show tha...
In 1967, Erdős asked for the greatest chromatic number, $f(n)$, amongst all $n$-vertex, triangle-fre...
AbstractThe relation of chromatic aspects and the existence of certain induced subgraphs of a triang...
AbstractAlthough the chromatic number of a graph is not known in general, attempts have been made to...
A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g w...
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
A graph with chromatic number k is called k-chromatic. Using computational methods, we show that the...
AbstractBy applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two c...
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