{"title":"小锦标赛的注射同态的复杂性和注射定向着色的复杂性","authors":"Russell Campbell, N. E. Clarke, G. MacGillivray","doi":"10.4236/ojdm.2023.131001","DOIUrl":null,"url":null,"abstract":". Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings\",\"authors\":\"Russell Campbell, N. E. Clarke, G. MacGillivray\",\"doi\":\"10.4236/ojdm.2023.131001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.\",\"PeriodicalId\":61712,\"journal\":{\"name\":\"离散数学期刊(英文)\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"离散数学期刊(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/ojdm.2023.131001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/ojdm.2023.131001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Complexity of Injective Homomorphisms to Small Tournaments, and of Injective Oriented Colourings
. Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.
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