{"title":"Nullhomotopic and Generating Knight's Tours on Non-Orientable Surfaces","authors":"Bradley Forrest, Zachary Lague","doi":"arxiv-2406.05226","DOIUrl":null,"url":null,"abstract":"We investigate closed knight's tours on M\\\"obius strip and Klein bottle chess\nboards. In particular, we characterize the board dimensions that admit tours\nthat are nullhomotopic and the board dimensions that admit tours that realize\ngenerators of the fundamental groups of each of the surfaces.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"208 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.05226","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate closed knight's tours on M\"obius strip and Klein bottle chess
boards. In particular, we characterize the board dimensions that admit tours
that are nullhomotopic and the board dimensions that admit tours that realize
generators of the fundamental groups of each of the surfaces.