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Computation of lucky number of planar graphs is NP-hard

Ahadi, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ipl.2011.11.002
  3. Publisher: 2012
  4. Abstract:
  5. A lucky labeling of a graph G is a function l:V(G)→N, such that for every two adjacent vertices v and u of G, σ w∼vl(w)≠ σ w∼ul(w) (x∼y means that x is joined to y). A lucky number of G, denoted by η(G), is the minimum number k such that G has a lucky labeling l:V(G)→{1,⋯,k}. We prove that for a given planar 3-colorable graph G determining whether η(G)=2 is NP-complete. Also for every k≥2, it is NP-complete to decide whether η(G)=k for a given graph G
  6. Keywords:
  7. Lucky labeling ; Adjacent vertices ; Graph coloring ; Graph G ; NP Complete ; NP-hard ; Planar graph ; Graph theory ; Computational complexity
  8. Source: Information Processing Letters ; Volume 112, Issue 4 , February , 2012 , Pages 109-112 ; 00200190 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0020019011003048