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Brahim Benmedjdoub, Isma Bouchemakh and Éric Sopena

R eferences [1] G. Agnarsson and M.M. Halldórsson, Coloring powers of planar graphs , SIAM J. Discrete Math. 16 (2003) 651–662. doi:10.1137/S0895480100367950 [2] M. Bonamy, B. Lévêque and A. Pinlou, 2 -distance coloring of sparse graphs , J. Graph Theory 77 (2014) 190–218. doi:10.1002/jgt.21782 [3] M. Bonamy, B. Lévêque and A. Pinlou, Graphs with maximum degree ∆ ≥ 17 and maximum average degree less than 3 are list 2 -distance (∆ + 2) -colorable , Discrete Math. 317 (2014) 19–32. doi:10.1016/j.disc.2013.10.022 [4] O

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Oleg V. Borodin and Anna O. Ivanova

). [4] O.V. Borodin, H.J. Broersma, A.N. Glebov and J. van den Heuvel The structure of plane triangulations in terms of stars and bunches, Diskretn. Anal. Issled. Oper. 8 (2001) 15-39 (in Russian). [5] O.V. Borodin, A.N. Glebov, A.O. Ivanova, T.K. Neustroeva and V.A. Tashkinov, Sufficient conditions for the 2-distance (_ + 1)-colorability of plane graphs, Sib. Elektron. Mat. Izv. 1 (2004) 129-141 (in Russian). [6] O.V. Borodin and A.O. Ivanova, 2-distance (_ + 2)-coloring of planar graphs with girth six and _ ≥ 18, Discrete Math. 309

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Gerard Jennhwa Chang, Mickael Montassier, Arnaud Pêche and André Raspaud

References [1] L.D. Andersen, The strong chromatic index of a cubic graph is at most 10, Discrete Math. 108 (1992) 231-252. doi:10.1016/0012-365X(92)90678-9 [2] K. Appel and W. Haken, Every planar map is four colorable. Part I. Discharging, Illinois J. Math. 21 (1977) 429-490. [3] K. Appel and W. Haken, Every planar map is four colorable. Part II. Reducibility, Illinois J. Math. 21 (1977) 491-567. [4] C.L. Barrett, G. Istrate, V.S.A. Kumar, M.V. Marathe, S. Thite, and S. Thulasidasan, Strong edge

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Nibedita Mandal and Pratima Panigrahi

References [1] P.C. Fishburn and F.S. Roberts, No-hole L(2, 1)-colorings, Discrete Appl. Math. 130 (2003) 513-519. doi:10.1016/S0166-218X(03)00329-9 [2] J.P. Georges, D.W. Mauro and M.A. Whittlesey, Relating path coverings to vertex labellings with a condition at distance two, Discrete Math. 135 (1994) 103-111. doi:10.1016/0012-365X(93)E0098-O [3] J.R. Griggs and R.K. Yeh, Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586-595. doi:10.1137/0405048 [4] R. Laskar

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Nibedita Mandal and Pratima Panigrahi

R eferences [1] F.-H. Chang, M.-L. Chia, D. Kuo, S.-C. Liaw and M.-H. Tsai, L (2, 1)- labelings of subdivisions of graphs , Discrete Math. 338 (2015) 248–255. doi:10.1016/j.disc.2014.09.006 [2] G.J. Chang and C. Lu, Distance-two labelings of graphs , European J. Combin. 24 (2003) 53–58. doi:10.1016/S0195-6698(02)00134-8 [3] P.C. Fishburn and F.S. Roberts, No-hole L (2, 1)- colorings , Discrete Appl. Math. 130 (2003) 513–519. doi:10.1016/S0166-218X(03)00329-9 [4] J.R. Griggs and R.K. Yeh, Labelling graphs with a condition at

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Jennifer Loe, Danielle Middelbrooks, Ashley Morris and Kirsti Wash

References [1] A. Bickle and B. Phillips, t-tone colorings of graphs, submitted (2011). [2] D. Cranston, J. Kim and W. Kinnersley, New results in t-tone colorings of graphs, Electron. J. Comb. 20(2) (2013) #17. [3] D. Bal, P. Bennett, A. Dudek and A. Frieze, The t-tone chromatic number of random graphs, Graphs Combin. 30 (2013) 1073-1086. doi:10.1007/s00373-013-1341-9 [4] N. Fonger, J. Goss, B. Phillips and C. Segroves, Math 6450: Final Report, (2011). http

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Stanislav Jendrol’, Mirko Horňák and Roman Soták

and A. Pinlou, 2-distance coloring of sparse graphs, J. Graph Theory 77 (2014) 190-218. doi: 10.1002/jgt.21782 [5] R.A. Brualdi and J.J. Quinn Massey, Incidence and strong edge colorings of graphs, Discrete Math. 122 (1993) 51-58. doi: 10.1016/0012-365X(93)90286-3 [6] I. Fabrici, S. Jendrol’ and M. Vrbjarová, Unique-maximum edge-colouring of plane graphs with respect to faces, Discrete Appl. Math. 185 (2015) 239-243. doi: 10.1016/j.dam.2014.12.002 [7] W. Goddard, Acyclic colorings of planar graphs, Discrete Math. 91

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Stanislav Jendroľ and Lucia Kekeňáková

R eferences [1] O. Amini, L. Esperet and J. van den Heuvel, A unified approach to distance-two colouring of planar graphs , in: Proc. SODA 2009 273–282. doi:10.1137/1.9781611973068.31 10.1137/1.9781611973068.31 [2] K. Appel and W. Haken, Every planar graph is four colorable, Part I: Discharging , Illinois J. Math. 21 (1977) 429–490. [3] K. Appel and W. Haken, Every planar graph is four colorable, Part II: Reducibility , Illinois J. Math. 21 (1977) 491–567. [4] J. Azarija, R. Erman, D. Kráľ, M. Krnc and L. Stacho, Cyclic colorings

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Wayne Goddard, Robert Melville and Honghai Xu

, A survey on the distance-colouring of graphs, Discrete Math. 308 (2008) 422-426. doi: 10.1016/j.disc.2006.11.059 [5] J.-M. Laborde, Sur le nombre domatique du n-cube et une conjecture de Zelinka, European J. Combin. 8 (1987) 175-177. doi: 10.1016/S0195-6698(87)80008-2 [6] P.M. Weichsel, Dominating sets in n-cubes, J. Graph Theory 18 (1994) 479-488. doi: 10.1002/jgt.3190180506 [7] B. Zelinka, Domatic numbers of cube graphs, Math. Slovaca 32 (1982) 117-119.

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Éric Sopena and Jiaojiao Wu

References [1] I. Algor and N. Alon, The star arboricity of graphs, Discrete Math. 75 (1989) 11-22. doi:10.1016/0012-365X(89)90073-3 [2] R.A. Brualdi and J.J. Quinn Massey, Incidence and strong edge colorings of graphs, Discrete Math. 122 (1993) 51-58. doi:10.1016/0012-365X(93)90286-3 [3] P. Erdős and J. Nešetřil, Problem, In: Irregularities of Partitions, G. Hal´asz and V.T. S´os (Eds.) (Springer, New-York) 162-163. [4] G. Fertin, E. Goddard and A. Raspaud, Acyclic and k-distance