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2007 | 27 | 3 | 389-400
Tytuł artykułu

Monochromatic kernel-perfectness of special classes of digraphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce the concept of monochromatic kernel-perfect digraph, and we prove the following two results:
(1) If D is a digraph without monochromatic directed cycles, then D and each $α_v,v ∈ V(D)$ are monochromatic kernel-perfect digraphs if and only if the composition over D of $(α_v)_{v ∈ V(D)}$ is a monochromatic kernel-perfect digraph.
(2) D is a monochromatic kernel-perfect digraph if and only if for any B ⊆ V(D), the duplication of D over B, $D^B$, is a monochromatic kernel-perfect digraph.
Wydawca
Rocznik
Tom
27
Numer
3
Strony
389-400
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-01-17
poprawiono
2007-06-11
zaakceptowano
2007-06-11
Twórcy
  • Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México
  • Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1369
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