Coloring Uniform Hypergraphs With Few Edges
A hypergraph is b-simple if no two distinct edges share more than b vertices. Let m(r, t, g) denote the minimum number of edges in an r-uniform non-t-colorable hypergraph of girth at least g. Erdos and Lovasz proved that m(r, t, 3) >= t(2(r-2))/16r(r - 1)(2) and m(r, t, g)   0 and sufficiently large r, every r-uniform b-simple hypergraph H with maximum edge-degree at most t(r) r(1-epsilon) is t-colorable. Some results hold for list coloring, as well. (C) 2009 Wiley Periodicals, Inc. Random Struct. Alg., 35, 348-368, 2009
edge-degree hypergraph coloring maximum degree small size