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A deletion game on hypergraphs. (English) Zbl 0728.90106

Let H be a finite, simple hypergraph and \(\Gamma\) (H) be the game in which players alternately delete either a vertex or an edge (with all vertices contained in the edge). As in Nim, the first player unable to move loses. The authors solve \(\Gamma\) (H) when H is a disjoint union of hypergraphs which are (1) P-uniform, P-partite; (2) cycles; and (3) complete multipartite graphs.

MSC:

91A43 Games involving graphs
05C65 Hypergraphs
91A05 2-person games
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References:

[1] Berge, C., (Graphs and Hypergraphs (1976), North-Holland: North-Holland Amsterdam), translated by E. Minieka · Zbl 0483.05029
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