A note on list improper coloring planar graphs |
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| Affiliation: | Institute of Mathematics, Academia Sinica, Nankang, Taipei 115, Taiwan, R.O.C.;Department of Mathematics, Hong Kong Baptist University Kowloon, Hong Kong;Department of Mathematics, Liaoning University Shenyang 110036, P.R. China;Department of Mathematics, Nanjing University Nanjing 210093, P.R. China |
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| Abstract: | A graph G is called (k, d)*-choosable if, for every list assignment L satisfying |L(v)| = k for all v ϵ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles and l-cycles for some l ϵ {5, 6, 7} is (3, 1)*-choosable. |
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