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- W3082874598 abstract "A family of sets is intersecting if any two sets in the family intersect. Given a graph G and an integer r≥1, let I(r)(G) denote the family of independent sets of size r of G. For a vertex v of G, the family of independent sets of size r that contain v is called an r-star. Then G is said to be r-EKR if no intersecting subfamily of I(r)(G) is bigger than the largest r-star. Let n be a positive integer, and let G consist of the disjoint union of n paths each of length 2. We prove that if 1≤r≤n∕2, then G is r-EKR. This affirms a longstanding conjecture of Holroyd and Talbot for this class of graphs and can be seen as an analogue of a well-known theorem on signed sets, proved using different methods, by Deza and Frankl and by Bollobás and Leader. Our main approach is a novel probabilistic extension of Katona’s elegant cycle method, which might be of independent interest." @default.
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- W3082874598 date "2020-12-01" @default.
- W3082874598 modified "2023-10-10" @default.
- W3082874598 title "An Erdős–Ko–Rado theorem for unions of length 2 paths" @default.
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- W3082874598 doi "https://doi.org/10.1016/j.disc.2020.112121" @default.
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