On(3,1)-choosability of planar graphs without adjacent short cycles

Discrete Applied Mathematics - Tập 162 - Trang 159-166 - 2014
Min Chen1, André Raspaud2
1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2LaBRI UMR CNRS 5800, Université Bordeaux I, 33405 Talence Cedex, France

Tài liệu tham khảo

Cowen, 1986, Defective colorings of graphs in surfaces: partitions into subgraphs of bounded valency, J. Graph Theory, 10, 187, 10.1002/jgt.3190100207 Cushing, 2010, Planar graphs are 1-relaxed, 4-choosable, European J. Combin., 31, 1385, 10.1016/j.ejc.2009.11.013 Dong, 2009, A note on list improper coloring of plane graphs, Discrete Appl. Math., 157, 433, 10.1016/j.dam.2008.06.023 Eaton, 1999, Defective list colorings of planar graphs, Bull. Inst. Combin. Appl., 25, 40 Erdős, 1979, Choosability in graphs, Congr. Numer., 26, 125 Lih, 2001, A note on list improper coloring planar graphs, Appl. Math. Lett., 14, 269, 10.1016/S0893-9659(00)00147-6 Šrekovski, 1999, List improper colourings of planar graphs, Combin. Probab. Comput., 8, 293, 10.1017/S0963548399003752 Šrekovski, 1999, A Gröstzsch-type theorem for list colorings with impropriety one, Combin. Probab. Comput., 8, 493, 10.1017/S096354839900396X Šrekovski, 2000, List improper colorings of planar graphs with prescribed girth, Discrete Math., 214, 221, 10.1016/S0012-365X(99)00145-4 Vizing, 1976, Vertex coloring with given colors, Diskret. Analiz., 29, 3 Xu, 2007, Every toroidal graph without adjacent triangles is (4,1)∗-choosable, Discrete Appl. Math., 155, 74, 10.1016/j.dam.2006.04.042 Zhang, 2012, A (3,1)∗-choosable theorem on toroidal graphs, Discrete Appl. Math., 160, 332, 10.1016/j.dam.2011.10.019