Kernels by monochromatic paths and the color-class digraph
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 273-281.

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An m-colored digraph is a digraph whose arcs are colored with m colors. A directed path is monochromatic when its arcs are colored alike.
Keywords: kernel, kernel by monochromatic paths, the color-class digraph
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Galeana-Sánchez, Hortensia. Kernels by monochromatic paths and the color-class digraph. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 273-281. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a4/

[1] J.M. Le Bars, Counterexample of the 0-1 law for fragments of existential second-order logic; an overview, Bull. Symbolic Logic 9 (2000) 67-82, doi: 10.2307/421076.

[2] J.M. Le Bars, The 0-1 law fails for frame satisfiability of propositional model logic, Proceedings of the 17th Symposium on Logic in Computer Science (2002) 225-234, doi: 10.1109/LICS.2002.1029831.

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

[4] 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.

[5] A.S. Fraenkel, Combinatorial game theory foundations applied to digraph kernels, Electronic J. Combin. 4 (2) (1997) #R10.

[6] A.S. Fraenkel, Combinatorial games: selected bibliography with a succint gourmet introduction, Electronic J. Combin. 14 (2007) #DS2.

[7] 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.

[8] 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.

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

[10] 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.

[11] 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.

[12] G. Gutin and J. Bang-Jensen, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, London, 2001).

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

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

[15] J. von Leeuwen, Having a Grundy Numbering is NP-complete, Report 207 Computer Science Department, University Park, PA, 1976, Pennsylvania State University.

[16] 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.

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

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