RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
Graphs, Combinatorics, Algorithms and Optimization
Page(s) 2619 - 2637
Published online 16 October 2023
  • M. Behzad, Graphs and their chromatic numbers, Ph.D. thesis, Michigan State University, East Lansing, MI, USA (1965). [Google Scholar]
  • G. Brinkmann, M. Preissmann and D. Sasaki, Snarks with total chromatic number 5. Discret. Math. Theor. Comput. Sci. 17 (2015) 369–382. [Google Scholar]
  • C.N. Campos, S. Dantas and C.P. De Mello, The total-chromatic number of some families of snarks. Discret. Math. 311 (2011) 984–988. [CrossRef] [Google Scholar]
  • A. Cavicchioli, T.E. Murgolo, B. Ruini and F. Spaggiari, Special classes of snarks. Acta Appl. Math. 76 (2003) 56–88. [Google Scholar]
  • S. Dantas, C.M.H. De Figueiredo, G. Mazzuoccolo, M. Preissmann, V.F. dos Santos and D. Sasaki, On the equitable total chromatic number of cubic graphs. Discret. Appl. Math. 209 (2016) 84–91. [CrossRef] [Google Scholar]
  • L. Esperet and G. Mazzuoccolo, On cubic bridgeless graphs whose edge-set cannot be covered by four perfect matchings. In Vol. 16 of the Seventh European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB’13). CRM Series, edited by J. Nešetřil and M. Pellegrini. Edizioni della Normale, Pisa (2013) 47–51. [CrossRef] [Google Scholar]
  • C.M.H. Figueiredo, R. Machado, U.S. Souza and A. Zorzi, Even-power of cycles with many vertices are Type 1 total colorable. Electron. Notes Theor. Comput. Sci. 346 (2019) 747–758. [CrossRef] [Google Scholar]
  • M. Gardner, Mathematical games: Snarks, boojums and other conjectures related to the fourcolor-map theorem. Sci. Am. 234 (1976) 126–130. [CrossRef] [Google Scholar]
  • M.K. Goldberg, Construction of class 2 graphs with maximum vertex degree 3. J. Combin. Theory Ser. B 31 (1981) 282–291. [CrossRef] [MathSciNet] [Google Scholar]
  • J. Hägglund, On Snarks that are far from beeing 3-edge-colorable. Electron. J. Comb. 3 (2016) 23. [Google Scholar]
  • R. Isaacs, Infinite Families of Nontrivial Trivalent Graphs Which Are Not Tait Colorable. Am. Math. Mon. 82 (1975) 221–239. [CrossRef] [Google Scholar]
  • R. Isaacs, Loupekine’s snarks: a bifamily of non Tait colorable graphs, Technical Report 263, Dpt. of Math. Sci., The Johns Hopkins University, Maryland, USA (1976). [Google Scholar]
  • M. Kochol, Snarks without small cycles. J. Combin. Theory Ser. B 67 (1996) 34–47. [CrossRef] [MathSciNet] [Google Scholar]
  • M. Rosenfeld, On the total coloring of certain graphs. Isr. J. Math. 9 (1971) 396–402. [CrossRef] [Google Scholar]
  • D. Sasaki, Uma família infinita de snarks Tipo 1, In Vol. 5 of Proceeding Series of the Brazilian Society of Applied and Computational Mathematics, N. 1, 2017. CNMAC, Gramado (2016) 1–6. [Google Scholar]
  • D. Sasaki, S. Dantas, C.M.H. De Figueiredo and M. Preissmann, The hunting of a snark with total chromatic number 5. Discret. Appl. Math. 164 (2014) 470–481. [CrossRef] [Google Scholar]
  • N. Vijayaditya, On total chromatic number of a graph. J. London Math. Soc. 3 (1971) 405–408. [CrossRef] [Google Scholar]
  • V.G. Vizing, On an estimate of the chromatic class of a p-graph. Diskret. Analiz. 3 (1964) 25–30. [Google Scholar]
  • W.F. Wang, Equitable total coloring of graphs with maximum degree. Graphs Combin. 18 (2002) 677–685. [CrossRef] [MathSciNet] [Google Scholar]

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