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Christopher Duffy, Gary MacGillivray, Pascal Ochem and André Raspaud

-families are dense, Theoret. Comput. Sci. 17 (1982) 29-41. doi: 10.1016/0304-3975(82)90129-3 [22] J. Wu, Some results on the incidence coloring number of a graph, Discrete Math. 309 (2009) 3866-3870. doi: 10.1016/j.disc.2008.10.027 [23] K. Young, 2-Dipath and Proper 2-Dipath Colouring (Masters Thesis, University of Victoria, 2009).

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Wayne Goddard, Kirsti Wash and Honghai Xu

References [1] M. Axenovich and P. Iverson, Edge-colorings avoiding rainbow and monochromatic subgraphs, Discrete Math. 308 (2008) 4710-4723. doi:10.1016/j.disc.2007.08.092 [2] M. Axenovich, T. Jiang and A. Kündgen, Bipartite anti-Ramsey numbers of cycles, J. Graph Theory 47 (2004) 9-28. doi:10.1002/jgt.20012 [3] Cs. Bujtás, E. Sampathkumar, Zs. Tuza, C. Dominic and L. Pushpalatha, Vertex coloring without large polychromatic stars, Discrete Math. 312 (2012) 2102-2108. doi:10.1016/j.disc.2011

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Eric Andrews, Laars Helenius, Daniel Johnston, Jonathon VerWys and Ping Zhang

References [1] L. Addario-Berry, R.E.L. Aldred, K. Dalal and B.A. Reed, Vertex colouring edge partitions, J. Combin. Theory (B) 94 (2005) 237-244. doi:10.1016/j.jctb.2005.01.001 [2] M. Anholcer, S. Cichacz and M. Milaniˇc, Group irregularity strength of connected graphs, J. Comb. Optim., to appear. doi:10.1007/s10878-013-9628-6 [3] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular networks, Congr. Numer. 64 (1988) 187-192. [4] G. Chartrand, L. Lesniak and P

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Anna Małafiejska and Michał Małafiejski

References [1] N. Alon, C. McDiarmid and B. Reed, Star arboricity, Combinatorica 12 (1992) 375-380. doi: 10.1007/BF01305230 [2] A. Asratian and R. Kamalian, Investigation on interval edge-colorings of graphs, J. Combin. Theory Ser. B 62 (1994) 34-43. doi: 10.1006/jctb.1994.1053 [3] R.A. Brualdi and J.Q. Massey, Incidence and strong edge colorings of graphs, Discrete Math. 122 (1993) 51-58. doi: 10.1016/0012-365X(93)90286-3 [4] M. Hosseini Dolama, E. Sopena and X. Zhu, Incidence coloring of k

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T. Karthick and C.R. Subramanian

References [1] M.O. Albertson, G.G. Chappell, H.A. Kierstead, A. Kündgen and R. Ramamurthi, Coloring with no 2-colored P4’s, Electron. J. Combin. 11 (2004) #R26. [2] N.R. Aravind and C.R. Subramanian, Bounds on vertex colorings with restrictions on the union of color classes, J. Graph Theory 66 (2011) 213-234. doi:10.1002/jgt.20501 [3] M.I. Burstein, Every 4-valent graph has an acyclic 5-coloring, Soobshcheniya Akademii Nauk Gruzinskoi SSR, 93 (1979) 21-24 (in Russian). [4] T.F. Coleman

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Gary Chartrand, Sean English and Ping Zhang

, Bull. Inst. Combin. Appl. 76 (2016) 69–84. [5] G. Chartrand and P. Zhang, Chromatic Graph Theory (Chapman & Hall/CRC Press, Boca Raton, FL, 2009). [6] O. Favaron, H. Li and R. H. Schelp, Strong edge colorings of graphs , Discrete Math. 159 (1996) 103–109. doi:10.1016/0012-365X(95)00102-3 [7] P.G. Tait, Remarks on the colouring of maps , Proc. Royal Soc. Edinburgh 10 (1880) 501–503, 729. doi:10.1017/S0370164600044643

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Július Czap and Peter Mihók

References [1] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, 2008). doi:10.1007/978-1-84628-970-5 [2] M. Borowiecki, A. Kemnitz, M. Marangio and P. Mihók, Generalized total colorings of graphs, Discuss. Math. Graph Theory 31 (2011) 209-222. doi:10.7151/dmgt.1540 [3] I. Broere, S. Dorfling and E. Jonck, Generalized chromatic numbers and additive hereditary properties of graphs, Discuss. Math. Graph Theory 22 (2002) 259-270. doi:10.7151/dmgt.1174 [4] M.J. Dorfling and S. Dorfling

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Piotr Formanowicz and Krzysztof Tanaś

-valent graph has an acyclic 5-coloring. Soobsc. Akad. Nauk Gruzin. SSR, 93:21_24, 1979. [10] Havet F. Muller T. Cohen, N. Acyclic edge-colouring of planar graphs. Technical report, Institut National de Recherche en Informatique et en Automatique, March 2009. [11] Grotschel M. Koster A. Eisenblatter, A. Frequency planning and rami_cations of coloring. Technical report, Konrad-Zuse-Zentrum fur Informationstechnik Berlin, Takustrasse 7, D-14196 Berlin-Dahlem, Germany, December 2000. [12] Rubin A.L. Taylor H. Erdos, P

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Mieczysław Borowiecki and Izak Broere

References [1] O.V. Borodin, On acyclic colorings of planar graphs, Discrete Math. 25 (1979) 211-236. doi:10.1016/0012-365X(79)90077-3 [2] O.V. Borodin, A.V. Kostochka and D.R. Woodall, Acyclic colourings of planar graphs with large girth, J. Lond. Math. Soc. 60 (1999) 344-352. doi:10.1112/S0024610799007942 [3] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50. doi:10.7151/dmgt.1037 [4] M

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Ismail Sahul Hamid and Malairaj Rajeswari

R eferences [1] S. Arumugam, J. Bagga and K.R. Chandrasekar, On dominator colorings in graphs , Proc. Indian Acad. Sci. Math. Sci. 122 (2012) 561–571. doi:10.1007/s12044-012-0092-5 [2] S. Arumugam, T.W. Haynes, M.A. Henning and Y. Nigussie, Maximal independent sets in minimum colorings , Discrete Math. 311 (2011) 1158–1163. doi:10.1016/j.disc.2010.06.045 [3] G. Chartrand and Lesniak, Graphs and Digraphs, Fourth Edition (CRC Press, Boca Raton, 2005). [4] R. Gera, On dominator coloring in graphs , Graph Theory Notes N.Y. 52 (2007