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A relation between choosability and uniquely list colorability

Akbari, S ; Sharif University of Technology | 2006

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jctb.2005.12.001
  3. Publisher: 2006
  4. Abstract:
  5. Let G be a graph with n vertices and m edges and assume that f : V ( G ) → N is a function with ∑v ∈ V ( G ) f ( v ) = m + n. We show that, if we can assign to any vertex v of G a list Lv of size f ( v ) such that G has a unique vertex coloring with these lists, then G is f-choosable. This implies that, if ∑v ∈ V ( G ) f ( v ) > m + n, then there is no list assignment L such that | Lv | = f ( v ) for any v ∈ V ( G ) and G is uniquely L-colorable. Finally, we prove that if G is a connected non-regular multigraph with a list assignment L of edges such that for each edge e = u v, | Le | = max { d ( u ), d ( v ) }, then G is not uniquely L-colorable and we conjecture that this result holds for any graph. © 2005 Elsevier Inc. All rights reserved
  6. Keywords:
  7. List coloring ; Uniquely ; Choosability
  8. Source: Journal of Combinatorial Theory. Series B ; Volume 96, Issue 4 , 2006 , Pages 577-583 ; 00958956 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0095895605001668