Games without repetitions on trees and multitrees
type: Item
instance of: scholarly article
title: Games without repetitions on trees and multitrees
zbMATH Open document ID: 0795.90100
DOI: 10.1007/BF01201457
author: Jerzy Michael
author: W. Szwiec
author: Zyta Dziechcińska-Halamoda
published in: Archiv der Mathematik
publication date: 1994-09-04T00:00:00Z
review text: We consider two-person games of the type NIM on a simple graph, where each edge may be used at most once during the playing of the game. We solve a certain problem of game partition into winning and losing vertices in the class of trees and multi-trees. The characterization of trees in which each vertex is a winning position is given. Moreover, we present an algorithm finding the game partition of a tree. Finally, we show that the game partition problem for multi-trees can be reduced to certain trees.
Mathematics Subject Classification ID: 91A43
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 493382
zbMATH Keywords: NIM
zbMATH Keywords: simple graph
zbMATH Keywords: winning and losing vertices
zbMATH Keywords: trees
zbMATH Keywords: multi-trees
MaRDI profile type: Publication
cites work: Games without repetitions on digraphs
cites work: Q4766829
cites work: Q3241018
full work available at URL: https://doi.org/10.1007/bf01201457
OpenAlex ID: W2005040176
description: scientific article; zbMATH DE number 493382