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Maximum Cycle Packing in Eulerian Graphs Using Local Traces

References [1] S. Antonakopulos and L. Zhang, Approximation algorithms for grooming in optical network design, Theoret. Comput. Sci. 412 (2011) 3738-3751. doi:10.1016/j.tcs.2011.03.034 [2] F. Bäbler, Über eine spezielle Klasse Euler’scher Graphen, Comment. Math. Helv. 27 (1953) 81-100. doi:10.1007/BF02564555 [3] V. Bafna and P.A. Pevzner, Genome rearrangement and sorting by reversals, SIAM J. Comput. 25 (1996) 272-289. doi:10.1137/S0097539793250627 [4] A. Caprara, Sorting permutations by

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Outpaths of Arcs in Regular 3-Partite Tournaments

Appl. Math. 95 (1999) 273–277. doi:10.1016/S0166-218X(99)00080-3 [5] L. Volkmann, Multipartite tournaments: a survey , Discrete Math. 307 (2007) 3097–3129. doi:10.1016/j.disc.2007.03.053 [6] G. Xu, S. Li, Q. Guo and H. Li, Notes on cycles through a vertex or an arc in regular 3 -partite tournaments , Appl. Math. Lett. 25 (2012) 662–664. doi:10.1016/j.aml.2011.09.075 [7] G. Zhou and K. Zhang, Outpaths of arcs in multipartite tournaments , Acta Math. Appl. Sin. (Engl. Ser.) 17 (2001) 361–365.

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Perturbations in a Signed Graph and its Index

. Cvetković, P. Rowlinson and S. Simić, An Introduction to the Theory of Graph Spectra (Cambridge University Press, Cambridge, 2010). [5] W.H. Haemars and E. Spence, Enumeration of cospectral graphs , European J. Combin. 25 (2004) 199–211. doi:10.1016/S0195-6698(03)00100-8 [6] T. Koledin and Z. Stanić, Connected signed graphs of fixed order, size, and number of negative edges with maximal index , Linear Multilinear Algebra 65 (2017) 2187–2198. doi:10.1080/03081087.2016.1265480 [7] B.D. McKay and A. Piperno, Practical graph isomorphism, II, J

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The Existence Of P≥3-Factor Covered Graphs

of length at least two, J. Combin. Theory Ser. B 88 (2003) 195-218. doi: 10.1016/S0095-8956(03)00027-3 [9] M. Kano, G.Y. Katona and Z. Király, Packing paths of length at least two, Discrete Math. 283 (2004) 129-135. doi: 10.1016/j.disc.2004.01.016 [10] M. Kano, H. Lu and Q. Yu, Component factors with large components in graphs, Appl. Math. Lett. 23 (2010) 385-389. doi: 10.1016/j.aml.2009.11.003 [11] M. Kouider and S. Ouatiki, Sufficient condition for the existence of an even [a, b]- factor in graph, Graphs Combin. 29

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Oriented Chromatic Number of Cartesian Products and Strong Products of Paths

] É. Sopena, The chromatic number of oriented graphs, J. Graph Theory 25 (1997) 191-205. doi: 10.1002/(SICI)1097-0118(199707)25:3h191::AID-JGT3i3.0.CO;2-G [15] É. Sopena, There exist oriented planar graphs with oriented chromatic number at least sixteen, Inform. Process. Lett. 81 (2002) 309-312. doi: 10.1016/S0020-0190(01)00246-0 [16] É. Sopena, Upper oriented chromatic number of undirected graphs and oriented col- orings of product graphs, Discuss. Math. Graph Theory 32 (2012) 517-533. doi: 10.7151/dmgt.1624 [17] É

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Decompositions of Plane Graphs Under Parity Constrains Given by Faces

edges of a graph by . . . , Colloquia Mathematica Societatis Janos Bolyai, 60. Sets, Graphs and Numbers (1991) 583-610. [9] D.P. Sanders and Y. Zhao, Planar graphs of maximum degree seven are class I, J. Combin. Theory (B) 83 (2001) 201-212. doi:10.1006/jctb.2001.2047 [10] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz 3 (1964) 25-30. [11] L. Zhang, Every planar graph with maximum degree 7 is class I, Graphs Combin. 16 (2000) 467-495. doi:10.1007/s003730070009

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Independent Detour Transversals in 3-Deficient Digraphs

References [1] S.A. van Aardt, G. Dlamini, J. Dunbar, M. Frick, and O. Oellermann, The directed path partition conjecture, Discuss. Math. Graph Theory 25 (2005) 331-343. doi:10.7151/dmgt.1286 [2] S.A. van Aardt, J.E. Dunbar, M. Frick, P. Katreniˇc, M.H. Nielsen, and O.R. Oellermann, Traceability of k-traceable oriented graphs, Discrete Math. 310 (2010) 1325-1333. doi:10.1016/j.disc.2009.12.022 [3] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, London, 2001

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On the Independence Number of Edge Chromatic Critical Graphs

-481. [7] D.P. Sanders and Y. Zhao, Planar graphs with maximum degree seven are Class I, J. Combin. Theory (B) 83 (2001) 201-212. doi:0.1006/jctb.2001.2047 [8] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964) 25-30 (in Russian). [9] V.G. Vizing, Some unsolved problems in graph theory, Uspekhi Mat. Nauk 23 (1968) 117-134, Russian Math. Surveys 23 (1968) 125-142. doi:10.1070/RM1968v023n06ABEH001252 [10] D.R. Woodall, The independence number of an edge chromatic critical graph, J

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Inverse Problem on the Steiner Wiener Index

.L. Puertas, Steiner distance and convexity in graphs , European J. Combin. 29 (2008) 726–736. doi:10.1016/j.ejc.2007.03.007 [6] G. Chartrand, O.R. Oellermann, S.L. Tian and H.B. Zou, Steiner distance in graphs , Časopis Pest. Mat. 114 (1989) 399–410. [7] L. Chen, X. Li and M. Liu, The ( revised ) Szeged index and the Wiener index of a nonbipartite graph , European J. Combin. 36 (2014) 237–246. doi:10.1016/j.ejc.2013.07.019 [8] P. Dankelmann, O.R. Oellermann and H.C. Swart, The average Steiner distance of a graph , J. Graph Theory 22 (1996

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On (p, 1)-Total Labelling of Some 1-Planar Graphs

, 2002). [9] F. Havet and M.-L. Yu, ( p, 1) -total labelling of graphs , Discrete Math. 308 (2008) 496–513. doi:10.1016/j.disc.2007.03.034 [10] L. Kowalik, J.-S. Sereni and R. Škrekovski, Total-coloring of plane graphs with maximum degree nine , SIAM J. Discrete Math. 22 (2008) 1462–1479. doi:10.1137/070688389 [11] S.G. Kobourov, G. Liotta and F. Montecchiani, An annotated bibliography on 1 -planarity , Comput. Sci. Rev. 25 (2017) 49–67. doi:10.1016/j.cosrev.2017.06.002 [12] M. Montassier and A. Raspaud, ( d, 1) -total labeling of

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