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On uniquely k-list colorable planar graphs, graphs on surfaces, and regular graphs

Abdolmaleki, M ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-018-1879-7
  3. Publisher: Springer Tokyo , 2018
  4. Abstract:
  5. A graph G is called uniquelyk-list colorable (UkLC) if there exists a list of colors on its vertices, say L= { Sv∣ v∈ V(G) } , each of size k, such that there is a unique proper list coloring of G from this list of colors. A graph G is said to have propertyM(k) if it is not uniquely k-list colorable. Mahmoodian and Mahdian (Ars Comb 51:295–305, 1999) characterized all graphs with property M(2). For k≥ 3 property M(k) has been studied only for multipartite graphs. Here we find bounds on M(k) for graphs embedded on surfaces, and obtain new results on planar graphs. We begin a general study of bounds on M(k) for regular graphs, as well as for graphs with varying list sizes. © 2018, Springer Japan KK, part of Springer Nature
  6. Keywords:
  7. Graphs on surfaces ; Planar graphs ; Regular graphs ; Uniquely list colorable graphs
  8. Source: Graphs and Combinatorics ; Volume 34, Issue 3 , May , 2018 , Pages 383-394 ; 09110119 (ISSN)
  9. URL: https://rd.springer.com/article/10.1007/s00373-018-1879-7