Erdős-Ko-Rado theorem in Peisert-type graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911768495783936 |
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| author | Yip, Chi Hoi |
| author_facet | Yip, Chi Hoi |
| contents | The celebrated Erdős-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00745 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Erdős-Ko-Rado theorem in Peisert-type graphs Yip, Chi Hoi Combinatorics 05C25, 15A03, 51E15 The celebrated Erdős-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. |
| title | Erdős-Ko-Rado theorem in Peisert-type graphs |
| topic | Combinatorics 05C25, 15A03, 51E15 |
| url | https://arxiv.org/abs/2302.00745 |