{"title":"完美混合倾斜的充分条件","authors":"Eoin Hurley , Felix Joos , Richard Lang","doi":"10.1016/j.jctb.2024.08.007","DOIUrl":null,"url":null,"abstract":"<div><div>We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs <em>H</em> with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect <em>F</em>-tilings (for an arbitrary fixed graph <em>F</em>) by replacing the <em>F</em>-tiling with the aforementioned graphs <em>H</em>. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sufficient conditions for perfect mixed tilings\",\"authors\":\"Eoin Hurley , Felix Joos , Richard Lang\",\"doi\":\"10.1016/j.jctb.2024.08.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs <em>H</em> with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect <em>F</em>-tilings (for an arbitrary fixed graph <em>F</em>) by replacing the <em>F</em>-tiling with the aforementioned graphs <em>H</em>. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.</div></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series B\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S009589562400073X\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009589562400073X","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们开发了一种方法来研究完美混合倾斜的充分条件。我们的框架允许嵌入具有亚线性阶成分的有界阶图 H。作为推论,我们恢复并扩展了库恩(Kühn)和奥斯特胡斯(Osthus)的工作,即用上述图 H 替换 F-tiling,从而获得完美 F-tiling(对于任意固定图 F)的最小阶数充分条件。最后,我们在强意义上渐近地解决了孔洛斯的一个猜想。
We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs H with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect F-tilings (for an arbitrary fixed graph F) by replacing the F-tiling with the aforementioned graphs H. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.
期刊介绍:
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.