80
Views
1
CrossRef citations to date
0
Altmetric
Section A

On the size of critical graphs with small maximum degree

, , &
Pages 2142-2151 | Received 07 Jun 2013, Accepted 08 Jan 2014, Published online: 26 Mar 2014

References

  • L. Clark and D. Haile, Remarks on the size of critical edge chromatic graph, Discrete Math. 171 (1997), pp. 287–293. doi: 10.1016/S0012-365X(97)89166-2
  • S. Fiorini, Some remarks on a paper by vizing on critical graphs, Math. Proc. Cambridge Philos. Soc. 77 (1975), pp. 475–483. doi: 10.1017/S030500410005129X
  • S. Fiorini and R.J. Wilson, Edge Colorings of Graphs, Pitman, San Francisco, 1977.
  • K. Kayathri, On the size of edge-chromatic critical graphs, Graphs Combin. 10 (1994), pp. 139–144. doi: 10.1007/BF02986658
  • X.C. Li, Sizes of critical graphs with small maximum degrees, Graphs Combin. 22 (2006), pp. 503–513. doi: 10.1007/s00373-006-0679-7
  • S.C. Li and X.C. Li, Edge coloring of graphs with small maximum degrees, Discrete Math. 309 (2009), pp. 4843–4852. doi: 10.1016/j.disc.2008.07.006
  • R. Luo, L.Y. Miao, and Y. Zhao, The size of edge chromatic critical graphs with maximum degree 6, J. Graph Theory 60 (2009), pp. 149–171. doi: 10.1002/jgt.20351
  • L.Y. Miao, On the independence number of edge chromatic critical graphs, Ars Combin. 60 (2011), pp. 471–481.
  • D.P. Sanders and Y. Zhao, Planar graph with maximum degree 7 is of class 1, J. Comb. Theory B 83 (2001), pp. 20–212.
  • V.G. Vizing, Some unsolved problems in graph theory (in Russian), Uspekhi Mat. Nauk 23 (1968), pp. 117–134; English translation in Russian Math. Surveys 23 (1968), pp. 125–141.
  • D.R. Woodall, The average degree of an edge-chromatic critical graph ∐, J. Graph Theory 56 (2007), pp. 194–218. doi: 10.1002/jgt.20259
  • L. Zhang, Every planar graph with maximum degree 7 is of class 1, Graphs Combin. 16 (2000), pp. 467–495. doi: 10.1007/s003730070009
  • Y. Zhao, New lower bounds for the size of edge chromatic critical graphs, J. Graph Theory 46 (2004), pp. 81–92. doi: 10.1002/jgt.10173

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.