Colouring Planar Mixed Hypergraphs

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Colouring Planar Mixed Hypergraphs
A mixed hypergraph is a triple H = (V, C, D) where V is the vertex set and C and D are families of subsets of V , the C-edges and D-edges, respectively. A k-colouring of H is a mapping c : V [k] such that each C-edge has at least two vertices with a Common colour and each D-edge has at least two vertices of Different colours. H is called a planar mixed hypergraph if its bipartite representation is a planar graph. Classic graphs are the special case of mixed hypergraphs when C = and all the D-edges have size 2, whereas in a bi-hypergraph C = D. We investigate the colouring properties of planar mixed hypergraphs. Specifically, we show that maximal planar bi-hypergraphs are 2-colourable, find formulas for their chromatic polynomial and chromatic spectrum in terms of 2-factors in the dual, prove that their chromatic spectrum is gap-free and provide a sharp estimate on the maximum number of colours in a colouring. Supported by NSERC grant of Derek Corneil and the Fields Institute. This...
André Kündgen, Eric Mendelsohn, Vitaly
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2000
Authors André Kündgen, Eric Mendelsohn, Vitaly I. Voloshin
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