Peisert型图中的Erdõs–Ko–Rado定理

IF 0.5 4区数学 Q3 MATHEMATICS

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2023-02-01 DOI:10.4153/S0008439523000607

Chi Hoi Yip

{"title":"Peisert型图中的Erdõs–Ko–Rado定理","authors":"Chi Hoi Yip","doi":"10.4153/S0008439523000607","DOIUrl":null,"url":null,"abstract":"The celebrated Erd\\H{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square order) states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are Peisert-type graphs for which the EKR theorem fails to hold. In this paper, we show that the EKR theorem of Paley graphs extends to almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the stability results of the same flavor.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Erdős–Ko–Rado theorem in Peisert-type graphs\",\"authors\":\"Chi Hoi Yip\",\"doi\":\"10.4153/S0008439523000607\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The celebrated Erd\\\\H{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square order) states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are Peisert-type graphs for which the EKR theorem fails to hold. In this paper, we show that the EKR theorem of Paley graphs extends to almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the stability results of the same flavor.\",\"PeriodicalId\":55280,\"journal\":{\"name\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/S0008439523000607\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/S0008439523000607","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

著名的(方阶)Paley图的Erd\H{o}s-Ko-Rado (EKR)定理指出，所有最大团都是正则的，因为每个最大团都是由子域构造产生的。最近，Asgarli和Yip将这一结果推广到Peisert图和其他在连接集上具有良好代数性质的Peisert型图的Cayley图。另一方面，也有peisert型图，EKR定理对其不成立。本文证明了Paley图的EKR定理可以推广到几乎所有的peisert型伪Paley图。此外，我们还建立了相同风味的稳定性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Erdős–Ko–Rado theorem in Peisert-type graphs

The celebrated Erd\H{o}s-Ko-Rado (EKR) theorem for Paley graphs (of square order) states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are Peisert-type graphs for which the EKR theorem fails to hold. In this paper, we show that the EKR theorem of Paley graphs extends to almost all pseudo-Paley graphs of Peisert-type. Furthermore, we establish the stability results of the same flavor.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The Canadian Mathematical Bulletin was established in 1958 to publish original, high-quality research papers in all branches of mathematics and to accommodate the growing demand for shorter research papers. The Bulletin is a companion publication to the Canadian Journal of Mathematics that publishes longer papers. New research papers are published continuously online and collated into print issues four times each year. To be submitted to the Bulletin, papers should be at most 18 pages long and may be written in English or in French. Longer papers should be submitted to the Canadian Journal of Mathematics. Fondé en 1958, le Bulletin canadien de mathématiques (BCM) publie des articles d’avant-garde et de grande qualité dans toutes les branches des mathématiques, de même que pour répondre à la demande croissante d’articles scientifiques plus brefs. Le BCM se veut une publication complémentaire au Journal canadien de mathématiques, qui publie de longs articles. En ligne, il propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés quatre fois par année. Les textes présentés au BCM doivent compter au plus 18 pages et être rédigés en anglais ou en français. C’est le Journal canadien de mathématiques qui reçoit les articles plus longs.