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2005 | 25 | 3 | 407-417
Tytuł artykułu

Kernels in monochromatic path digraphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
(i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and
(ii) for each vertex x ∈ (V(D)-N) there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
In this paper is defined the monochromatic path digraph of D, MP(D), and the inner m-colouration of MP(D). Also it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner m-colouration of MP(D). A previous result is generalized.
Wydawca
Rocznik
Tom
25
Numer
3
Strony
407-417
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-08-03
poprawiono
2004-12-10
Twórcy
  • Instituto de Matemáticas, UNAM, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F. México
Bibliografia
  • [1] C. Berge, Graphs (North-Holland, Amsterdam, 1985).
  • [2] C. Berge and A. Ramachandra Rao, A combinatorial problem in logic, Discrete Math. 17 (1977) 23-26, doi: 10.1016/0012-365X(77)90018-8.
  • [3] P. Duchet, A sufficient condition for a digraph to be kernel-perfect, J. Graph Theory 11 (1987) 81-85, doi: 10.1002/jgt.3190110112.
  • [4] P. Duchet and H. Meyniel, Une généralization du théoréme de Richardson sur l'existence du noyaux dans les graphes orientés, Discrete Math. 43 (1983) 21-27, doi: 10.1016/0012-365X(83)90017-1.
  • [5] 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.
  • [6] H. Galeana-Sánchez, L. Pastrana Ramírez and H.A. Rincón-Mejía, Semikernels, quasikernels and Grundy functions in the line digraph, SIAM J. Disc. Math. 1 (1999) 80-83.
  • [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 and Xueliang Li, Semikernels and (k,l)-kernels in digraphs, SIAM J. Discrete Math. 11 (1998) 340-346, doi: 10.1137/S0895480195291370.
  • [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 L. Pastrana Ramírez, Kernels in edge coloured line digraph, Discuss. Math. Graph Theory 18 (1998) 91-98, doi: 10.7151/dmgt.1066.
  • [11] H. Galeana-Sánchez and José de Jesús García-Ruvalcaba, Kernels in the closure of coloured digraphs, Discuss. Math. Graph Theory 20 (2000) 243-254, doi: 10.7151/dmgt.1123.
  • [12] M. Harminc, Solutions and kernels of a directed graph, Math. Slovaca 32 (1982) 263-267.
  • [13] J. Von Neumann and O. Morgenstern, Theory of games and economic behavior (Princeton University Press, Princeton, NJ, 1944).
  • [14] 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.
  • [15] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1292
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