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On the chromatic number of generalized Kneser graphs and Hadamard matrices

Jafari, A ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2019.111682
  3. Publisher: Elsevier B.V , 2020
  4. Abstract:
  5. Let n>k>d be positive integers. The generalized Kneser graph K(n,k,d) is a graph whose vertices are all the subsets of size k in {1,…,n} and two subsets are adjacent if and only if they have less than d elements in common. For d=1 this is the classical Kneser graph whose chromatic number was calculated by Lovász in Lovász (1978). In this article, we use Hadamard matrices to show that for any integer r≥0, the chromatic number of K(2k+2r,k,d) is at most 8(r+d)2 for k≥4(r+d)2−r. This bound improves the previously known upper bounds drastically. © 2019 Elsevier B.V
  6. Keywords:
  7. Chromatic number ; Hadamard Matrices ; Kneser graphs
  8. Source: Discrete Mathematics ; Volume 343, Issue 2 , February , 2020
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0012365X19303607