A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866929722492977152 |
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| author | Gunderson, Karen Meagher, Karen Morris, Joy Pantangi, Venkata Raghu Tej Shirazi, Mahsa N |
| author_facet | Gunderson, Karen Meagher, Karen Morris, Joy Pantangi, Venkata Raghu Tej Shirazi, Mahsa N |
| contents | In this paper we introduce a new way of measuring the robustness of Erdős--Ko--Rado (EKR) Theorems on permutation groups. EKR-type results can be viewed as results about the independence numbers of certain corresponding graphs, namely the derangement graphs, and random subgraphs of these graphs have been used to measure the robustness of these extremal results. In the context of permutation groups, the derangement graphs are Cayley graphs on the permutation group in question. We propose studying extremal properties of subgraphs of derangement graphs, that are themselves Cayley graphs of the group, to measure robustness.
We present a variety of results about the robustness of the EKR property of various permutation groups using this new measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups Gunderson, Karen Meagher, Karen Morris, Joy Pantangi, Venkata Raghu Tej Shirazi, Mahsa N Combinatorics 05E30, 05C50, 05C25 In this paper we introduce a new way of measuring the robustness of Erdős--Ko--Rado (EKR) Theorems on permutation groups. EKR-type results can be viewed as results about the independence numbers of certain corresponding graphs, namely the derangement graphs, and random subgraphs of these graphs have been used to measure the robustness of these extremal results. In the context of permutation groups, the derangement graphs are Cayley graphs on the permutation group in question. We propose studying extremal properties of subgraphs of derangement graphs, that are themselves Cayley graphs of the group, to measure robustness. We present a variety of results about the robustness of the EKR property of various permutation groups using this new measure. |
| title | A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups |
| topic | Combinatorics 05E30, 05C50, 05C25 |
| url | https://arxiv.org/abs/2502.14582 |