同态全向图

IF 0.7 4区数学

Discrete Mathematics and Theoretical Computer Science Pub Date : 2023-10-02 DOI:10.46298/dmtcs.9957

Thomas Bellitto, Christopher Duffy, Gary MacGillivray

{"title":"同态全向图","authors":"Thomas Bellitto, Christopher Duffy, Gary MacGillivray","doi":"10.46298/dmtcs.9957","DOIUrl":null,"url":null,"abstract":"Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homomorphically Full Oriented Graphs\",\"authors\":\"Thomas Bellitto, Christopher Duffy, Gary MacGillivray\",\"doi\":\"10.46298/dmtcs.9957\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.\",\"PeriodicalId\":55175,\"journal\":{\"name\":\"Discrete Mathematics and Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/dmtcs.9957\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/dmtcs.9957","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

同态满图是指每个同态象同构于一个子图的图。我们以两种不同的方式将同态满的定义扩展到有向图。首先，我们证明了同态满向图是同态满图的拟传递取向。这反过来又为这些同态全面向图提供了有效的识别和构造算法。对于第二个问题，我们证明了相关的识别问题是gi困难的，并且确定图是否允许同态满方向的问题是np完全的。在此过程中，我们证明了判定两个给定的有向团是否同构的问题是gi完全的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Homomorphically Full Oriented Graphs

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics and Theoretical Computer Science 数学-计算机：软件工程

自引率

14.30%

发文量

期刊介绍： DMTCS is a open access scientic journal that is online since 1998. We are member of the Free Journal Network. Sections of DMTCS Analysis of Algorithms Automata, Logic and Semantics Combinatorics Discrete Algorithms Distributed Computing and Networking Graph Theory.