Fraenkel, Aviezri S.; Scheinerman, Edward R. A deletion game on hypergraphs. (English) Zbl 0728.90106 Discrete Appl. Math. 30, No. 2-3, 155-162 (1991). 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. Reviewer: M.Fox (East Lansing) Cited in 7 Documents MSC: 91A43 Games involving graphs 05C65 Hypergraphs 91A05 2-person games Keywords:Sprague-Grundy function; hypergraph; Nim; P-uniform; P-partite; cycles; complete multipartite graphs PDFBibTeX XMLCite \textit{A. S. Fraenkel} and \textit{E. R. Scheinerman}, Discrete Appl. Math. 30, No. 2--3, 155--162 (1991; Zbl 0728.90106) Full Text: DOI Online Encyclopedia of Integer Sequences: Table of Sprague-Grundy functions for a certain family of hypergraphs, read by antidiagonals. References: [1] Berge, C., (Graphs and Hypergraphs (1976), North-Holland: North-Holland Amsterdam), translated by E. Minieka · Zbl 0483.05029 [2] Berlekamp, E. R.; Conway, J. H.; Guy, R. K., Winning Ways (1982), Academic Press: Academic Press London · Zbl 0485.00025 [3] Gale, D., A curious Nim-type game, Amer. Math. Monthly, 81, 876-879 (1974) · Zbl 0295.90045 [4] Gale, D.; Neyman, A., Nim-type games, Internat. J. Game Theory, 11, 17-20 (1982) · Zbl 0508.90100 [5] Úlehla, J., A complete analysis of Von Neumann’s Hackendot, Internat. J. Game Theory, 9, 107-113 (1980) · Zbl 0433.90101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.