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On the complexity of unique list colourability and the fixing number of graphs

Daneshgar, A ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. Publisher: 2010
  3. Abstract:
  4. Let G be a finite simple x-chromatic graph and L = {Lu} u∈V(G) be a list assignment to its vertices with Lu {1.....X}- A list colouring problem (G, L) with a unique solution for which the sum Σu∈V(G) |Lu| is maximized, is called a maximum X-list assignment of G. In this paper, we prove a Circuit Simulation Lemma that, strictly speaking, makes it possible to simulate any Boolean function by effective 3-colourings of a graph that is polynomial-time constructable from the Boolean function itself. We use the lemma to simply prove some old results as corollaries, and also we prove that the following decision problem, related to the computation of the fixing number of a graph [Daneshgar 1997, Daneshgar and Naserasr, Ars Combin. 69 (2003)], is Σ 2P-complete
  5. Keywords:
  7. Source: Ars Combinatoria ; Volume 97 , 2010 , Pages 301-319 ; 03817032 (ISSN)