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Ramsey- and Turán-type problems were always strongly related to each other. Motivated by an observation of Paul Erdős, it was Turán who started the systematic investigation of the applications of extremal graph theory in geometry and analysis. This led the second author to some results and...
A combinatorial approach developed by the author in 1959 is used to explain the connection between limit process and combinatorial properties of families of finite sets.
The circular chromatic number χ c (G) of a graph G (also known as ‘the star-chromatic number’), is a natural generalization of the chromatic number of a graph. In this paper, we survey results on this topic, concentrating on the relations among the circular chromatic number, the chromatic...
An oriented k -coloring of an oriented graph G (that is a digraph with no cycle of length 2) is a partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the same subset and (ii) all the arcs between any two subsets have the same direction. We survey the main...
A ( strongly ) Helly graph * is a connected graph for which any finite (resp. finite or infinite) family of pairwise non-disjoint balls has a non-empty intersection. Strongly Helly graphs are important objects of the category of simple graphs with contractions (i.e., maps that preserve or...
The oddness of a multigraph was introduced by M. Kochol and the author. It is always a nonnegative even number and for cubic multigraphs G, it measures how far G is away from being 3-edge colourable. M. Kochol and the author proved that each bridgeless multigraph of oddness at most 2 contains a...
For a positive integer k, a graph G is k-ordered if for every ordered set of k vertices, there is a cycle that encounters the vertices of the set in the given order. If the cycle is also a hamiltonian cycle, then G is said to be k-ordered hamiltonian. This was a concept that was introduced by Ng...
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