{"title":"图具有强宇称因子的充分条件","authors":"Sizhong Zhou, Yuli Zhang","doi":"10.1051/ro/2023147","DOIUrl":null,"url":null,"abstract":"A graph G has a strong parity factor F if for every subset X ⊆ V ( G ) with | X | even, G contains a spanning subgraph F such that δ ( F ) ≥ 1, d F ( u ) ≡ 1 (mod 2) for any u ∈ X , and d F ( v ) ≡ 0 (mod 2) for any v ∈ V ( G ) \\ X . In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"307 1","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sufficient conditions for graphs to have strong parity factors\",\"authors\":\"Sizhong Zhou, Yuli Zhang\",\"doi\":\"10.1051/ro/2023147\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph G has a strong parity factor F if for every subset X ⊆ V ( G ) with | X | even, G contains a spanning subgraph F such that δ ( F ) ≥ 1, d F ( u ) ≡ 1 (mod 2) for any u ∈ X , and d F ( v ) ≡ 0 (mod 2) for any v ∈ V ( G ) \\\\ X . In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.\",\"PeriodicalId\":54509,\"journal\":{\"name\":\"Rairo-Operations Research\",\"volume\":\"307 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rairo-Operations Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/ro/2023147\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rairo-Operations Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/ro/2023147","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
摘要
图G有一个强宇称因子F，如果对每一个子集X V (G)有| × |偶，G包含一个生成子图F，使得δ (F)≥1，对于任意u∈X, F (u)≡1 (mod 2)，对于任意V∈V (G) \ X, F (V)≡0 (mod 2)。在本文中，我们首先提供了具有强奇偶因子的图的大小条件。然后给出了保证图具有强宇称因子的一个韧性条件。
Sufficient conditions for graphs to have strong parity factors
A graph G has a strong parity factor F if for every subset X ⊆ V ( G ) with | X | even, G contains a spanning subgraph F such that δ ( F ) ≥ 1, d F ( u ) ≡ 1 (mod 2) for any u ∈ X , and d F ( v ) ≡ 0 (mod 2) for any v ∈ V ( G ) \ X . In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor.
期刊介绍：
RAIRO-Operations Research is an international journal devoted to high-level pure and applied research on all aspects of operations research. All papers published in RAIRO-Operations Research are critically refereed according to international standards. Any paper will either be accepted (possibly with minor revisions) either submitted to another evaluation (after a major revision) or rejected. Every effort will be made by the Editorial Board to ensure a first answer concerning a submitted paper within three months, and a final decision in a period of time not exceeding six months.
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