Monochromatic kernel-perfectness of special classes of digraphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 389-400.

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In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results:
Keywords: kernel, kernel by monochromatic paths, composition, duplication
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Galeana-Sánchez, Hortensia; Ramírez, Luis. Monochromatic kernel-perfectness of special classes of digraphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 389-400. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a0/

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

[2] M. Blidia, P. Duchet, H. Jacob, F. Maffray and H. Meyniel, Some operations preserving the existence of kernels, Discrete Math. 205 (1999) 211-216, doi: 10.1016/S0012-365X(99)00026-6.

[3] M. Borowiecki and A. Szelecka, One-factorizations of the generalized Cartesian product and of the X-join of regular graphs, Discuss. Math. Graph Theory 13 (1993) 15-19.

[4] M. Burlet and J. Uhry, Parity Graphs, Annals of Discrete Math. 21 (1984) 253-277

[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] 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.

[7] H. Galeana-Sánchez, On monochromatic paths and monochromatics cycles in edge coloured tournaments, Discrete Math. 156 (1996) 103-110, doi: 10.1016/0012-365X(95)00036-V.

[8] H. Galeana-Sánchez and V. Neumann-Lara, On the dichromatic number in kernel theory, Math. Slovaca 48 (1998) 213-219.

[9] 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.

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

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

[12] M. Kucharska, On (k,l)-kernel perfectness of special classes of digraphs, Discussiones Mathematicae Graph Theory 25 (2005) 103-119, doi: 10.7151/dmgt.1265.

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

[14] 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.

[15] 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.

[16] J. von Neumann and O. Morgenstern, Theory of games and economic behavior (Princeton University Press, Princeton, 1944).

[17] A. Włoch and I. Włoch, On (k,l)-kernels in generalized products, Discrete Math. 164 (1997) 295-301, doi: 10.1016/S0012-365X(96)00064-7.

[18] I. Włoch, On kernels by monochromatic paths in the corona of digraphs, preprint.