Geodesic
Monochromatic paths and monochromatic sets of arcs in bipartite tournaments
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 349-360.

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We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours and all of them are used. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices there is no monochromatic path between them and for every vertex v in V(D)∖N there is a monochromatic path from v to some vertex in N. We denote by A⁺(u) the set of arcs of D that have u as the initial endpoint.
Keywords: m-coloured bipartite tournaments, kernel by monochromatic paths, semikernel of D modulo i by monochromatic paths 
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Galeana-Sánchez, Hortensia; Rojas-Monroy, R.; Zavala, B. Monochromatic paths and monochromatic sets of arcs in bipartite tournaments. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 349-360. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a9/

[1] C. Berge, Graphs (North Holland, Amsterdam, New York, 1985).

[2] E. Boros and V. Gurvich, Perfect graphs, kernels, and cores of cooperative games, Discrete Math. 306 (2006) 2336-2354, doi: 10.1016/j.disc.2005.12.031.

[3] P. Duchet, Graphes noyau-parfaits, Ann. Discrete Math. 9 (1980) 93-101, doi: 10.1016/S0167-5060(08)70041-4.

[4] P. Duchet, Classical Perfect Graphs, An introduction with emphasis on triangulated and interval graphs, Ann. Discrete Math. 21 (1984) 67-96.

[5] P. Duchet and H. Meyniel, A note on kernel-critical graphs, Discrete Math. 33 (1981) 103-105, doi: 10.1016/0012-365X(81)90264-8.

[6] A.S. Fraenkel, Combinatorial games: selected bibliography with a succinct gourmet introduction, Elec. J. Combin. (surveys) #DS2.

[7] H. Galeana-Sánchez, On monochromatic paths and monochromatic cycles in edge coloured tournaments, Discrete Math. 156 (1996) 103-112, doi: 10.1016/0012-365X(95)00036-V.

[8] H. Galeana-Sánchez, Kernels in edge coloured digraphs, Discrete Math. 184 (1998) 87-99, doi: 10.1016/S0012-365X(97)00162-3.

[9] H. Galeana-Sánchez and J.J. García Ruvalcaba, Kernels in the clousure of coloured digraphs, Discuss. Math. Graph Theory 20 (2000) 243-354, doi: 10.7151/dmgt.1123.

[10] H. Galena-Sánchez and V. Neumann-Lara, On kernel and semikernels of digraphs, Discrete Math. 48 (1984) 67-76, doi: 10.1016/0012-365X(84)90131-6.

[11] H. Galeana-Sánchez and V. Neumann-Lara, On kernel-perfect critical digraphs, Discrete Math. 59 (1986) 257-265, doi: 10.1016/0012-365X(86)90172-X.

[12] H. Galeana-Sánchez and R. Rojas-Monroy, On monochromatic paths and monochromatic 4-cycles in edge coloured bipartite tournaments, Discrete Math. 285 (2004) 313-318, doi: 10.1016/j.disc.2004.03.005.

[13] H. Galeana-Sánchez and R. Rojas-Monroy, Monochromatic paths and most 2-coloured arc sets in edge-coloured tournaments, Graphs and Combin. 21 (2005) 307-317, doi: 10.1007/s00373-005-0618-z.

[14] G. Hahn, P. Ille and R. Woodrow, Absorbing sets in arc-coloured tournaments, Discrete Math. 283 (2004) 93-99, doi: 10.1016/j.disc.2003.10.024.

[15] T.W. Haynes, T. Hedetniemi and P.J. Slater, editors, Domination in Graphs (Advanced Topics, Marcel Dekker Inc., 1998).

[16] T.W. Haynes, T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker Inc., 1998).

[17] M. Kucharska, On (k,l)-kernels of orientations of special graphs, Ars Combin. 60 (2001) 137-147.

[18] M. Kucharska and M. Kwaśnik, On (k,l)-kernels of superdigraphs of Pₘ and Cₘ, Discuss. Math. Graph Theory 21 (2001) 95-109, doi: 10.7151/dmgt.1135.

[19] M. KwaŚnik, The generalization of Richardson's Theorem, Discuss. Math. Graph Theory IV (1981) 11-14.

[20] M. KwaŚnik, On (k,l)-kernels of exclusive disjunction, cartesian sum and normal product of two directed graphs, Discuss. Math. Graph Theory V (1982) 29-34.

[21] S. Minggang, On monochromatic paths in m-coloured tournaments, J. Combin. Theory (B) 45 (1988) 108-111, doi: 10.1016/0095-8956(88)90059-7.

[22] M.V. Neumann-Lara, Seminúcleos de una digráfica, An. Inst. Mat. UNAM 11 (1971) 55-62.

[23] M. Richardson, Solutions of irreflexive relations, Ann. Math. 58 (1953) 573, doi: 10.2307/1969755.

[24] M. Richardson, Extensions theorems for solutions of irreflexive relations, Proc. Nat. Acad. Sci. USA 39 (1953) 649, doi: 10.1073/pnas.39.7.649.

[25] B. Sands, N. Sauer and R. Woodrow, On monochromatic paths in edge-coloured digraphs, J. Combin. Theory (B) 33 (1982) 271-275, doi: 10.1016/0095-8956(82)90047-8.

[26] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301.

[27] I. Włoch, On imp-sets and kernels by monochromatic paths in duplication, Ars Combin. 83 (2007) 93-99.

[28] I. Włoch, On kernels by monochromatic paths in the corona of digraphs, Cent. Eur. J. Math. 6 (2008) 537-542.