A new upper bound on the acyclic chromatic indices of planar graphs

European Journal of Combinatorics - Tập 34 - Trang 338-354 - 2013
Weifan Wang1, Qiaojun Shu1, Yiqiao Wang2
1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2School of Management, Beijing University of Chinese Medicine, Beijing 100029, China

Tài liệu tham khảo

Alon, 1991, Acyclic coloring of graphs, Random Structures Algorithms, 2, 277, 10.1002/rsa.3240020303 Alon, 2001, Acyclic edge colorings of graphs, J. Graph Theory, 37, 157, 10.1002/jgt.1010 Basavaraju, 2008, Acyclic edge coloring of subcubic graphs, Discrete Math., 308, 6650, 10.1016/j.disc.2007.12.036 Basavaraju, 2009, Acyclic edge coloring of graphs with maximum with degree 4, J. Graph Theory, 61, 192, 10.1002/jgt.20376 Basavaraju, 2011, Acyclic edge-coloring of planar graphs, SIAM J. Discrete Math., 25, 463, 10.1137/090776676 Borowiecki, 2010, Acyclic edge coloring of planar graphs without short cycles, Discrete Math., 310, 1445, 10.1016/j.disc.2009.06.007 Dong, 2010, Some results on acyclic edge coloring of plane graphs, Inform. Process. Lett., 110, 887, 10.1016/j.ipl.2010.07.019 Fiamčik, 1978, The acyclic chromatic class of a graph, Math. Slovaca, 28, 139 Fiedorowicz, 2008, About acyclic edge colourings of planar graphs, Inform. Process. Lett., 108, 412, 10.1016/j.ipl.2008.07.016 Hou, 2012, Acyclic edge coloring of planar graphs without small cycles, Graphs Combin., 28, 215, 10.1007/s00373-011-1043-0 Hou, 2010, Acyclic edge chromatic number of outerplanar graphs, J. Graph Theory, 64, 22, 10.1002/jgt.20436 Hou, 2009, Acyclic edge colorings of planar graphs and series–parallel graphs, Sci. China Ser. A, 52, 605, 10.1007/s11425-008-0124-x M. Molloy, B. Reed, Further algorithmic aspects of Lovász local lemma, in: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 524–529. Muthu, 2007, Acyclic edge colouring of outerplanar graphs, Lecture Notes in Comput. Sci., 4508, 144, 10.1007/978-3-540-72870-2_14 Něsetřil, 2005, The acyclic edge chromatic number of a random d-regular graph is d+1, J. Graph Theory, 49, 69, 10.1002/jgt.20064 Shu, 2012, Acyclic chromatic indices of planar graphs with girth at least five, J. Comb. Optim., 23, 140, 10.1007/s10878-010-9354-2 Shu, 2012, Acyclic edge coloring of planar graphs without 5-cycles, Discrete Appl. Math., 160, 1211, 10.1016/j.dam.2011.12.016 Skulrattanakulchai, 2004, Acyclic colorings of subcubic graphs, Inform. Process. Lett., 92, 161, 10.1016/j.ipl.2004.08.002 Vizing, 1964, On an estimate of the chromatic index of a p-graph, Diskret Analiz., 3, 25 Wang, 2011, Acyclic chromatic indices of K4-minor free graphs, Sci. China Ser. A, 41, 733 Wang, 2011, Acyclic chromatic indices of planar graphs with large girth, Discrete Appl. Math., 59, 1239, 10.1016/j.dam.2011.03.017 Yu, 2009, Acyclic acyclic edge coloring of planar graphs with large girth, Theoret. Comput. Sci., 410, 5196, 10.1016/j.tcs.2009.08.015