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Greedy defining sets of graphs

Zaker, M ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. Publisher: 2001
  3. Abstract:
  4. For a graph G and an order σ on V(G), we define a greedy defining set as a subset S of V(G) with an assignment of colors to vertices in S, such that the pre-coloring can be extended to a χ(G)-coloring of G by the greedy coloring of (G, σ). A greedy defining set of a χ(G)-coloring C of G is a greedy defining set, which results in the coloring C (by the greedy procedure). We denote the size of a greedy defining set of C with minimum cardinality by GDN (G, σ, C). In this paper we show that the problem of determining GDN(G, σ, C), for an instance (G, σ, C) is an NP-complete problem
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 23 , 2001 , Pages 231-235 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/23/ocr-ajc-v23-p231.pdf