Equitable colorings of non-uniform simple hypergraphsстатья
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Дата последнего поиска статьи во внешних источниках: 8 января 2017 г.
Аннотация:Abstract
The paper is devoted to the combinatorial problem concerning equitable colorings of non-uniform simple hypergraphs. Let H=(V,E) be a hypergraph, a coloring with r colors of its vertex set V is called equitable if it is proper (i.e. none of the edges is monochromatic) and the cardinalities of the color classes differ by at most one. We show that if H is a simple hypergraph with minimum edge-cardinality n and
∑e∈Er1−|e|≥cn√,
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for some absolute constant c>0 , then H has an equitable r-coloring.