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Some relations among term rank, clique number and list chromatic number of a graph

Akbari, S ; Sharif University of Technology | 2006

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2004.11.028
  3. Publisher: Elsevier , 2006
  4. Abstract:
  5. Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and term rank of G, by rk (G) and Rk (G), respectively. van Nuffelen conjectured that for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour. In 2002, Fishkind and Kotlov proved that for any graph G, χ (G) ≤ Rk (G). Here we improve this upper bound and show that χl (G) ≤ (rk (G) + Rk (G)) / 2, where χl (G) is the list chromatic number of G. © 2006 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Mathematical programming ; Number theory ; Set theory ; Chromatic numbers ; K-choosable ; Term ranks ; Graph theory
  8. Source: Discrete Mathematics ; Volume 306, Issue 23 SPEC. ISS , 2006 , Pages 3078-3082 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0012365X06004018