On 3-choosability of planar graphs without certain cycles

Authors:
Haihui Zhang;Zhiren Sun
Affiliations:
School of Mathematics and Computer Science, Nanjing Normal University, 122, Ninghai Road, Nanjing 210097, PR China and Mathematics Department, Huaiyin Teachers College, 223001 Huaian, PR China;School of Mathematics and Computer Science, Nanjing Normal University, 122, Ninghai Road, Nanjing 210097, PR China
Venue:
Information Processing Letters
Year:
2008

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A note on 3-choosability of planar graphs

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Three-coloring planar graphs without short cycles

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RETRACTED ARTICLE: On 3-choosability of planar graphs with neither adjacent triangles nor 5-, 6- and 9-cycles

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Abstract

A graph G=(V,E) is L-colorable if for a given list assignment L={L(v):v@?V(G)}, there exists a proper coloring c of G such that c(v)@?L(v) for all v@?V. If G is L-colorable for every list assignment L with |L(v)|=k for all v@?V, then G is said to be k-choosable. In this paper, we prove that every planar graph with neither 5-, 6-, and 7-cycles nor triangles of distance less than 3, or with neither 5-, 6-, and 8-cycles nor triangles of distance less than 2 is 3-choosable.