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math.CO2025
Hilton-Milner Theorem for the -independent sets in a union of cliques
Karen Gunderson, Karen Meagher, Joy Morris +1
We give a Hilton-Milner Theorem for the -independent sets in the graph that is the union of copies of . That is, we determine the maximum intersecting families of -indep…
math.CO2025
A new measure of robustness of ErdÅs--Ko--Rado Theorems on permutation groups
Karen Gunderson, Karen Meagher, Joy Morris +2
In this paper we introduce a new way of measuring the robustness of ErdÅs--Ko--Rado (EKR) Theorems on permutation groups. EKR-type results can be viewed as results about the indep…
math.CO2024
Robustness of ErdÅs--Ko--Rado theorems on permutations and perfect matchings
Karen Gunderson, Karen Meagher, Joy Morris +2
The ErdÅs--Ko--Rado (EKR) theorem and its generalizations can be viewed as classifications of maximum independent sets in appropriately defined families of graphs, such as the Kne…