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arXiv · 2203.09696

Take-Away Impartial Combinatorial Games on Hypergraphs and Other Related Geometric and Discrete Structures

T. H. Molena
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Abstract

In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either a single vertex or a hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed. When a player chooses to remove one hyperedge, only that chosen hyperedge is removed. Whoever removes the last vertex wins the game. Following from the winning strategy for the Take-Away Impartial Combinatorial Games on only Oddly Uniform or only Evenly Uniform Hypergraphs, this paper is about the new winning strategy for Take-Away Games on neither Oddly nor Evenly Uniform Hypergraphs. These neither Oddly nor Evenly Uniform Hypergraphs, however, have to satisfy the specific given requirements.

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BibTeXRIS

T. H. Molena. 2022-03-18. Take-Away Impartial Combinatorial Games on Hypergraphs and Other Related Geometric and Discrete Structures. https://arxiv.org/abs/2203.09696

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