{"title":"Erdős-Gyárfás 猜想对无 P10 图形成立","authors":"","doi":"10.1016/j.disc.2024.114175","DOIUrl":null,"url":null,"abstract":"<div><p>The Erdős-Gyárfás conjecture asserts that every graph with minimum degree at least three has a cycle whose length is a power of 2. Let <em>G</em> be a graph with minimum degree at least 3. We show that if <em>G</em> contains no induced path of order 10, then <em>G</em> contains a cycle of length 4 or 8, and hence the conjecture holds in this case.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Erdős-Gyárfás conjecture holds for P10-free graphs\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114175\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Erdős-Gyárfás conjecture asserts that every graph with minimum degree at least three has a cycle whose length is a power of 2. Let <em>G</em> be a graph with minimum degree at least 3. We show that if <em>G</em> contains no induced path of order 10, then <em>G</em> contains a cycle of length 4 or 8, and hence the conjecture holds in this case.</p></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003066\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003066","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
厄尔多斯-希亚法斯猜想断言,每个最小度数至少为 3 的图都有一个长度为 2 的幂的循环。让 G 是一个最小度数至少为 3 的图。我们证明,如果 G 不包含阶数为 10 的诱导路径,那么 G 包含一个长度为 4 或 8 的循环,因此猜想在这种情况下成立。
The Erdős-Gyárfás conjecture holds for P10-free graphs
The Erdős-Gyárfás conjecture asserts that every graph with minimum degree at least three has a cycle whose length is a power of 2. Let G be a graph with minimum degree at least 3. We show that if G contains no induced path of order 10, then G contains a cycle of length 4 or 8, and hence the conjecture holds in this case.
期刊介绍:
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.