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English version: Journal of Applied and Industrial Mathematics, 2017, 11:1, 125129 

Volume 24, No 1, 2017, P. 2130 UDC 519.8
Keywords: list coloring, incidentor, $(k, l)$coloring. DOI: 10.17377/daio.2017.24.542 Ekaterina I. Vasilyeva ^{2} Received 24 May 2016 References[1] V. G. Vizing, Incidentor coloring of multigraphs in prescribed colors, Diskretn. Anal. Issled. Oper., Ser. 1, 7, No. 1, 32–39, 2000 [Russian].[2] V. G. Vizing, A bipartite interpretation of a directed multigraph in problems of the coloring of incidentors, Diskretn. Anal. Issled. Oper., Ser. 1, 9, No. 1, 27–41, 2002 [Russian]. [3] V. G. Vizing, Strict coloring of incidentors in undirected multigraphs, Diskretn. Anal. Issled. Oper., Ser. 1, 12, No. 3, 48–53, 2005 [Russian]. [4] V. G. Vizing, On the $(p, q)$coloring of incidentors of an undirected multigraph, Diskretn. Anal. Issled. Oper., Ser. 1, 12, No. 4, 23–39, 2005 [Russian]. [5] V. G. Vizing, L. S. Mel’nikov, and A. V. Pyatkin, On the $(k, l)$coloring of incidentors, Diskretn. Anal. Issled. Oper., Ser. 1, 7, No. 4, 29–37, 2000 [Russian]. [6] V. G. Vizing and A. V. Pyatkin, Incidentor coloring of multigraphs, in R. I. Tyshkevich, ed., Topics in Graph Theory, pp. 197–209, Urbana, USA, 2013 [Russian]. Available at http://www.math.uiuc.edu/˜kostochk/. Accessed Mar. 3, 2015. [7] A. V. Pyatkin, Some problems for optimizing the routing of messages in a local communication network, Diskretn. Anal. Issled. Oper., 2, No. 4, 74–79, 1995 [Russian]. Translated in A. D. Korshunov, ed., Operations Research and Discrete Analysis, pp. 227–232, Kluwer Acad. Publ., Dordrecht, 1997 (Math. Appl., Vol. 391). [8] A. V. Pyatkin, $(k, l)$Coloring of incidentors of cubic multigraphs, Diskretn. Anal. Issled. Oper., Ser. 1, 9, No. 1, 49–53, 2002 [Russian]. [9] A. V. Pyatkin, Some upper bounds for the incidentor $(k, l)$chromatic number, Diskretn. Anal. Issled. Oper., Ser. 1, 10, No. 2, 66–78, 2003 [Russian]. [10] A. V. Pyatkin, Upper and lower bounds for the incidentor $(k, l)$chromatic number, Diskretn. Anal. Issled. Oper., Ser. 1, 11, No. 1, 93–102, 2004 [Russian]. [11] A. V. Pyatkin, On (1, 1)coloring of incidentors of multigraphs of degree 4, Diskretn. Anal. Issled. Oper., Ser. 1, 11, No. 3, 59–62, 2004 [Russian]. [12] A. V. Pyatkin, On list incidentor coloring of a multigraph of degree 3, Diskretn. Anal. Issled. Oper., Ser. 1, 14, No. 3, 80–89, 2007 [Russian]. Translated in J. Appl. Ind. Math., 2, No. 4, 560565, 2008. [13] O. V. Borodin, A. V. Kostochka, and D. R. Woodall, List edge and list total colorings of multigraphs, J. Comb. Theory, Ser. B, 71, No. 2, 184–204, 1997. 

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