{"title":"给定阶数和最小阶数的弦图的最小尺寸","authors":"Xingzhi Zhan, Leilei Zhang","doi":"arxiv-2409.10261","DOIUrl":null,"url":null,"abstract":"A graph is chordal if it does not contain an induced cycle of length greater\nthan three. We determine the minimum size of a chordal graph with given order\nand minimum degree. In doing so, we have discovered interesting properties of\nchordal graphs.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The minimum size of a chordal graph with given order and minimum degree\",\"authors\":\"Xingzhi Zhan, Leilei Zhang\",\"doi\":\"arxiv-2409.10261\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A graph is chordal if it does not contain an induced cycle of length greater\\nthan three. We determine the minimum size of a chordal graph with given order\\nand minimum degree. In doing so, we have discovered interesting properties of\\nchordal graphs.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"31 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-2409.10261\",\"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-2409.10261","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The minimum size of a chordal graph with given order and minimum degree
A graph is chordal if it does not contain an induced cycle of length greater
than three. We determine the minimum size of a chordal graph with given order
and minimum degree. In doing so, we have discovered interesting properties of
chordal graphs.