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Hajós' theorem for list colorings of hypergraphs

Claude Benzaken, Sylvain Gravier, Riste Skrekovski (2003)

Discussiones Mathematicae Graph Theory

A well-known theorem of Hajós claims that every graph with chromathic number greater than k can be constructed from disjoint copies of the complete graph K k + 1 by repeated application of three simple operations. This classical result has been extended in 1978 to colorings of hypergraphs by C. Benzaken and in 1996 to list-colorings of graphs by S. Gravier. In this note, we capture both variations to extend Hajós’ theorem to list-colorings of hypergraphs.

Hypergraphs with large transversal number and with edge sizes at least four

Michael Henning, Christian Löwenstein (2012)

Open Mathematics

Let H be a hypergraph on n vertices and m edges with all edges of size at least four. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. Lai and Chang [An upper bound for the transversal numbers of 4-uniform hypergraphs, J. Combin. Theory Ser. B, 1990, 50(1), 129–133] proved that τ(H) ≤ 2(n+m)/9, while Chvátal and McDiarmid [Small transversals in hypergraphs, Combinatorica, 1992, 12(1), 19–26] proved that τ(H) ≤ (n + 2m)/6. In this paper, we characterize...

Hypergraphs with Pendant Paths are not Chromatically Unique

Ioan Tomescu (2014)

Discussiones Mathematicae Graph Theory

In this note it is shown that every hypergraph containing a pendant path of length at least 2 is not chromatically unique. The same conclusion holds for h-uniform r-quasi linear 3-cycle if r ≥ 2.

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