无射线图的强纳什-威廉斯定向定理

arXiv - MATH - Combinatorics Pub Date : 2024-09-16 DOI:arxiv-2409.10378

Max Pitz, Jacob Stegemann

{"title":"无射线图的强纳什-威廉斯定向定理","authors":"Max Pitz, Jacob Stegemann","doi":"arxiv-2409.10378","DOIUrl":null,"url":null,"abstract":"In 1960, Nash-Williams proved his strong orientation theorem that every\nfinite graph has an orientation in which the number of directed paths between\nany two vertices is at least half the number of undirected paths between them\n(rounded down). Nash-Williams conjectured that it is possible to find such\norientations for infinite graphs as well. We provide a partial answer by\nproving that all rayless graphs have such an orientation.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The strong Nash-Williams orientation theorem for rayless graphs\",\"authors\":\"Max Pitz, Jacob Stegemann\",\"doi\":\"arxiv-2409.10378\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 1960, Nash-Williams proved his strong orientation theorem that every\\nfinite graph has an orientation in which the number of directed paths between\\nany two vertices is at least half the number of undirected paths between them\\n(rounded down). Nash-Williams conjectured that it is possible to find such\\norientations for infinite graphs as well. We provide a partial answer by\\nproving that all rayless graphs have such an orientation.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10378\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10378","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

1960 年，纳什-威廉斯证明了他的强定向定理，即每个无限图都有一个定向，其中任何两个顶点之间的有向路径数至少是它们之间无向路径数的一半（四舍五入）。纳什-威廉姆斯猜想，无限图也有可能找到这样的定向。通过证明所有无射线图都有这样的方向，我们给出了部分答案。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The strong Nash-Williams orientation theorem for rayless graphs

In 1960, Nash-Williams proved his strong orientation theorem that every finite graph has an orientation in which the number of directed paths between any two vertices is at least half the number of undirected paths between them (rounded down). Nash-Williams conjectured that it is possible to find such orientations for infinite graphs as well. We provide a partial answer by proving that all rayless graphs have such an orientation.

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

arXiv - MATH - Combinatorics

自引率

0.00%

发文量

期刊最新文献

A note on connectivity in directed graphs Proof of a conjecture on graph polytope Generalized Andrásfai--Erdős--Sós theorems for odd cycles The repetition threshold for ternary rich words Isomorphisms of bi-Cayley graphs on generalized quaternion groups