Geodesic
Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 285-306.

Voir la notice de l'article provenant de la source Library of Science

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
Keywords: kernel, kernel by monochromatic paths, bipartite tournament 
@article{DMGT_2008_28_2_a5,
     author = {Galeana-Sanchez, Hortensia and Rojas-Monroy, Roc{\'\i}o},
     title = {Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {285--306},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a5/}
}
TY  - JOUR
AU  - Galeana-Sanchez, Hortensia
AU  - Rojas-Monroy, Rocío
TI  - Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2008
SP  - 285
EP  - 306
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a5/
LA  - en
ID  - DMGT_2008_28_2_a5
ER  - 
%0 Journal Article
%A Galeana-Sanchez, Hortensia
%A Rojas-Monroy, Rocío
%T Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments
%J Discussiones Mathematicae. Graph Theory
%D 2008
%P 285-306
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a5/
%G en
%F DMGT_2008_28_2_a5
Galeana-Sanchez, Hortensia; Rojas-Monroy, Rocío. Monochromatic paths and quasi-monochromatic cycles in edge-coloured bipartite tournaments. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 2, pp. 285-306. http://geodesic.mathdoc.fr/item/DMGT_2008_28_2_a5/

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

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

[3] 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.

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

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

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

[7] H. Galeana-Sánchez and J.J. García-Ruvalcaba, Kernels in the closure of coloured digraphs, Discuss. Math. Graph Theory 20 (2000) 243-254, doi: 10.7151/dmgt.1123.

[8] 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.

[9] H. Galeana-Sánchez and R. Rojas-Monroy, A counterexample to a conjecture on edge-coloured tournaments, Discrete Math. 282 (2004) 275-276, doi: 10.1016/j.disc.2003.11.015.

[10] 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.

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

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

[13] 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.

[14] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (Princeton University Press, Princeton, 1944).