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Rank, term rank and chromatic number of a graph

Akbari, S ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1016/j.crma.2004.12.003
  3. Publisher: 2005
  4. Abstract:
  5. Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by rk (G) and Rk (G), respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265-266], for any graph G, χ (G) ≤ rk (G). The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523-525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253-257] have proved that for any graph G, χ (G) ≤ Rk (G). In this Note we improve Fishkind-Kotlov upper bound and show that χ (G) ≤ rk(G)+Rk(G)/2. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved
  6. Keywords:
  8. Source: Comptes Rendus Mathematique ; Volume 340, Issue 3 , 2005 , Pages 181-184 ; 1631073X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S1631073X04005837?via%3Dihub