{"title":"Disconnected forbidden pairs force supereulerian graphs to be hamiltonian","authors":"","doi":"10.1016/j.disc.2024.114301","DOIUrl":null,"url":null,"abstract":"<div><div>A graph is said to be supereulerian if it has a spanning eulerian subgraph, i.e., a spanning connected even subgraph. A graph is called hamiltonian if it contains a spanning cycle. A graph is said to be <span><math><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></math></span>-free if it does not contain <em>R</em> or <em>S</em> as an induced subgraph. Yang et al. characterized all pairs of connected graphs <span><math><mi>R</mi><mo>,</mo><mi>S</mi></math></span> such that every supereulerian <span><math><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></math></span>-free graph is hamiltonian. In this paper, we consider disconnected forbidden graph <span><math><mi>R</mi><mo>,</mo><mi>S</mi></math></span>. We characterize all pairs of disconnected graphs <span><math><mi>R</mi><mo>,</mo><mi>S</mi></math></span> such that every supereulerian <span><math><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></math></span>-free graph of sufficiently large order is hamiltonian. Applying this result, we also characterize all forbidden pairs for the existence of a Hamiltonian cycle in 2-edge connected graphs.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-31","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/S0012365X24004321","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
Abstract
A graph is said to be supereulerian if it has a spanning eulerian subgraph, i.e., a spanning connected even subgraph. A graph is called hamiltonian if it contains a spanning cycle. A graph is said to be -free if it does not contain R or S as an induced subgraph. Yang et al. characterized all pairs of connected graphs such that every supereulerian -free graph is hamiltonian. In this paper, we consider disconnected forbidden graph . We characterize all pairs of disconnected graphs such that every supereulerian -free graph of sufficiently large order is hamiltonian. Applying this result, we also characterize all forbidden pairs for the existence of a Hamiltonian cycle in 2-edge connected graphs.
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.
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