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On the conjecture of planar graphs

Abdollahzadeh Ahangar|Pushpalatha
장전수학회 (Jangjeon Mathematical Society)|2010.01|Advanced Studies in Contemporary Mathematics|제20권 제1호|pp. 89-93

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참고문헌

키워드

planar graphgraph coloringlist coloringuniquely list colorable.
주제분류수학

초록

Let G be a graph. Suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists. Then G is called a uniquely k-list colorable graph. In this note we disprove a Conjecture for U3LC planar graphs which appeared in [3].

Abstract

Let G be a graph. Suppose that for each vertex v in G, there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists. Then G is called a uniquely k-list colorable graph. In this note we disprove a Conjecture for U3LC planar graphs which appeared in [3].

참고문헌 (7)

  1. N. Alon, "Restricted colorings of graphs. in: Surveys in com-binatorics, number 187 in London Math. Soc. LNS", pp.1~33 (1993)
  2. P. ErdÄos, "Choosability in graphs", In proceedings of west coast conferenc on combinatorics, graph theory, and computing, pp.125~157 (1979)
  3. Ch. Eslahchi, "Some concepts in list Coloring", Combinatorial Mathematics and Combinatorial Computing, 41, pp.151~160 (2002)
  4. D. Mojdeh, "The Graph K2,2,r has the property M (3) for 4≤ r ≥ 8", Bulletin of the ICA, pp.63~70 (2006)
  5. D. Mojdeh, "Graphs K1*4,5, K1*5,4, K1*4,4,K2,3,4 have the property M (3)", Ars Combinato-ria, pp.171~190 (2007)
  6. V. G. Vizing, "Coloring the vertices of graph in prescribed colors, In Diskret. Analiz, number 29 in Metody Diskret. Anal. v Teorii Kodov i Shem", 3~10 (1976)
  7. D. B. West, "Introduction to graph theory" (2003), Prentice Hall of India

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