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1998 | 18 | 1 | 91-98
Tytuł artykułu

Kernels in edge coloured line digraph

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the two following conditions (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and (ii) for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
Let D be an m-coloured digraph and L(D) its line digraph. The inner m-coloration of L(D) is the edge coloration of L(D) defined as follows: If h is an arc of D of colour c, then any arc of the form (x,h) in L(D) also has colour c.
In this paper 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 edge coloration of L(D).
Wydawca
Rocznik
Tom
18
Numer
1
Strony
91-98
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-27
poprawiono
1997-09-22
Twórcy
  • Instituto de Matemáticas, U.N.A.M., C.U., Circuito Exterior, D. F. 04510 México
  • Departamento de Matemáticas de la Facultad de Ciencias de la Universidad Nacional Autónoma de México, México, D.F.
Bibliografia
  • [1] C. Berge, Graphs (North Holland, Amsterdam, New York, 1985).
  • [2] 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.
  • [3] H. Galeana-Sánchez and J.J. García Ruvalcaba, Kernels in {C₃, T₃}-free arc colorations of Kₙ - e, submitted.
  • [4] 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.
  • [5] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1066
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