{"title":"没有5环的1-平面图是5简并的","authors":"Qingqin Wu , Weifan Wang , Jiangxu Kong","doi":"10.1016/j.amc.2025.129304","DOIUrl":null,"url":null,"abstract":"<div><div>A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is <em>k</em>-degenerate if each of its subgraphs contains a vertex of degree no greater than <em>k</em>. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"495 ","pages":"Article 129304"},"PeriodicalIF":3.4000,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"1-Planar graphs with no 5-cycles are 5-degenerate\",\"authors\":\"Qingqin Wu , Weifan Wang , Jiangxu Kong\",\"doi\":\"10.1016/j.amc.2025.129304\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is <em>k</em>-degenerate if each of its subgraphs contains a vertex of degree no greater than <em>k</em>. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.</div></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"495 \",\"pages\":\"Article 129304\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300325000311\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/20 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325000311","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is k-degenerate if each of its subgraphs contains a vertex of degree no greater than k. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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