CID 2003 Abstracts - Colourings, Independence and Domination

22 abstracts
ON PANCHROMATIC COLORINGS OF HYPERGRAPHS
Ewa Drgas-Burchardt
University of Zielona Góra, Poland
and
Ewa ̷Lazuka
Technical University of Lublin, Poland
Let H be a hypergraph and k ≥ 2 be a positive integer. A vertex k-coloring
of H is panchromatic if each of the k colors is used on every egde of H [1,2]. The
number of panchromatic k-colorings of H is given by a polynomial f k (H, λ) of
degree |V (H)| in λ, called the k-panchromatic polynomial of H.
We present the method of calculating the k-panchromatic polynomial of any
hypergraph. It uses the partitions of a graph induced by a k-subset of a fixed
edge of H into stable sets. We apply this method to several types of hypergraphs.
We also study some coefficients of f k (H, λ).
Keywords: panchromatic coloring of a hypergraph, chromatic polynomial of
a hypergraph.
AMS Subject Classification: 05C15.
References
[1] A.V. Kostochka, On a theorem of Erdös, Rubin, and Taylor on choosability
of complete bipartite graphs, The Electronic Journal of Combinatorics
9 (2002) #N9.
[2] A.V. Kostochka, D.R. Woodall, Density conditions for panchromatic colourings
of hypergraphs, Combinatorica 21 (2001) 515–541.