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Bipartitions of highly connected tournaments. (English) Zbl 1336.05050

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C35 Extremal problems in graph theory 05C40 Connectivity 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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##### References:
 [1] P. Hajnal, Partition of graphs with condition on the connectivity and minimum degree, Combinatorica, 3 (1983), pp. 95–99. · Zbl 0529.05030 [2] D. Kühn, J. Lapinskas, D. Osthus, and V. Patel, Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments, Proc. London Math. Soc. (3), 109 (2014), pp. 733–762. · Zbl 1302.05069 [3] D. Kühn and D. Osthus, Partitions of graphs with high minimum degree or connectivity, J. Combin. Theory Ser. B, 88 (2003), pp. 29–43. · Zbl 1045.05075 [4] D. Kühn, D. Osthus, and T. Townsend, Proof of a tournament partition conjecture and an application to \textup1-factors with prescribed cycle lengths, Combinatorica, to appear. [5] A. Pokrovskiy, Highly linked tournaments, J. Combin. Theory Ser. B, 115 (2015), pp. 339–347. · Zbl 1319.05063 [6] A. Pokrovskiy, Edge Disjoint Hamiltonian Cycles in Highly Connected Tournaments, preprint, arXiv:1406.7556. [7] A. Scott, Judicious partitions and related problems, in Surveys in Combinatorics 2005, London Math. Soc. Lecture Note Ser. 327, Cambridge University Press, Cambridge, 2005, pp. 95–117. · Zbl 1110.05084 [8] C. Thomassen, Hamiltonian-connected tournaments, J. Combin. Theory Ser. B, 28 (1980), pp. 142–163. · Zbl 0435.05026 [9] C. Thomassen, Graph decomposition with constraints on the connectivity and minimum degree, J. Graph Theory, 7 (1983), pp. 165–167. · Zbl 0515.05045 [10] C. Thomassen, Graph decomposition with applications to subdivisions and path systems modulo $$k$$, J. Graph Theory, 7 (1983), pp. 261–271. · Zbl 0515.05052 [11] C. Thomassen, Connectivity in tournaments, in Graph Theory and Combinatorics, a Volume in Honour of Paul Erdös, B. Bollobás, ed., Academic Press, London, 1984, pp. 305–313. [12] C. Thomassen, Configurations in graphs of large minimum degree, connectivity, or chromatic number, in Combinatorial Mathematics: Proceedings of the Third International Conference (New York, 1985), Ann. New York Acad. Sci. 555, New York Acad. Sci., New York, 1989, pp. 402–412.
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