Color-bounded hypergraphs, I: General results |
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Authors: | Csilla Bujtá s |
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Affiliation: | a Department of Computer Science, University of Pannonia, H-8200 Veszprém, Egyetem u. 10, Hungary b Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary |
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Abstract: | The concept of color-bounded hypergraph is introduced here. It is a hypergraph (set system) with vertex set X and edge set E={E1,…,Em}, where each edge Ei is associated with two integers si and ti such that 1≤si≤ti≤|Ei|. A vertex coloring φ:X→N is considered to be feasible if the number of colors occurring in Ei satisfies si≤|φ(Ei)|≤ti, for all i≤m.Color-bounded hypergraphs generalize the concept of ‘mixed hypergraphs’ introduced by Voloshin [V. Voloshin, The mixed hypergraphs, Computer Science Journal of Moldova 1 (1993) 45-52], and a recent model studied by Drgas-Burchardt and ?azuka [E. Drgas-Burchardt, E. ?azuka, On chromatic polynomials of hypergraphs, Applied Mathematics Letters 20 (12) (2007) 1250-1254] where only lower bounds si were considered.We discuss the similarities and differences between our general model and the more particular earlier ones. An important issue is the chromatic spectrum-strongly related to the chromatic polynomial-which is the sequence whose kth element is the number of allowed colorings with precisely k colors (disregarding color permutations). Problems concerning algorithmic complexity are also considered. |
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Keywords: | Hypergraph Vertex coloring Chromatic polynomial Feasible set Uniquely colorable hypergraph Mixed hypergraph |
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