Intersections of matroids
| Autor: | Aharoni, Ron, Berger, Eli, Guo, He, Kotlar, Dani |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study simplicial complexes (hypergraphs closed under taking subsets) that are the intersection of a given number k of matroids. We prove bounds on their chromatic numbers (the minimum number of edges required to cover the ground set) and their list chromatic numbers. Settling a conjecture of Kiraly and Berczi et. al., we prove that the list chromatic number is at most k times the chromatic number. Following the footsteps of Edmonds, who considered the case k=2, we study three polytopes associated with k-tuples of matroids, and prove bounds on the distances between them. The tools used are in part topological. Comment: 35 pages |
| Databáze: | arXiv |
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