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The existence of uniform hypergraphs for which the interpolation property of complete coloring fails

Haghparast, N ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2021.112722
  3. Publisher: Elsevier B.V , 2022
  4. Abstract:
  5. In 1967 Harary, Hedetniemi, and Prins showed that every graph G admits a complete t-coloring for every t with χ(G)≤t≤ψ(G), where χ(G) denotes the chromatic number of G and ψ(G) denotes the achromatic number of G which is the maximum number r for which G admits a complete r-coloring. Recently, Edwards and Rza̧żewski (2020) showed that this result fails for hypergraphs by proving that for every integer k with k≥9, there exists a k-uniform hypergraph H with a complete χ(H)-coloring and a complete ψ(H)-coloring, but no complete t-coloring for some t with χ(H)
  6. Keywords:
  7. Complete coloring ; Face hypergraph ; Hypergraph ; Triangulation
  8. Source: Discrete Mathematics ; Volume 345, Issue 3 , 2022 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0012365X21004350