Hypergraph Colouring and Degeneracy
نویسنده
چکیده
A hypergraph is d-degenerate if every subhypergraph has a vertex of degree at most d. A greedy algorithm colours every such hypergraph with at most d+ 1 colours. We show that this bound is tight, by constructing an r-uniform d-degenerate hypergraph with chromatic number d + 1 for all r ≥ 2 and d ≥ 1. Moreover, the hypergraph is triangle-free, where a triangle in an r-uniform hypergraph consists of three edges whose union is a set of r + 1 vertices.
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تاریخ انتشار 2014