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GC
2016
Springer

Spectrum of Mixed Bi-uniform Hypergraphs

3 years 17 days ago
Spectrum of Mixed Bi-uniform Hypergraphs
A mixed hypergraph is a triple H = (V, C, D), where V is a set of vertices, C and D are sets of hyperedges. A vertex-coloring of H is proper if C-edges are not totally multicolored and D-edges are not monochromatic. The feasible set S(H) of H is the set of all integers, s, such that H has a proper coloring with s colors. Bujt´as and Tuza [Graphs and Combinatorics 24 (2008), 1–12] gave a characterization of feasible sets for mixed hypergraphs with all C- and D-edges of the same size r, r ≥ 3. In this note, we give a short proof of a complete characterization of all possible feasible sets for mixed hypergraphs with all C-edges of size and all D-edges of size m, where , m ≥ 2. Moreover, we show that for every sequence (r(s))n s= , n ≥ , of natural numbers there exists such a hypergraph with exactly r(s) proper colorings using s colors, s = , . . . , n, and no proper coloring with more than n colors. Choosing = m = r this answers a question of Bujt´as and Tuza, and generalizes th...
Maria Axenovich, Enrica Cherubini, Torsten Ueckerd
Added 03 Apr 2016
Updated 03 Apr 2016
Type Journal
Year 2016
Where GC
Authors Maria Axenovich, Enrica Cherubini, Torsten Ueckerdt
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