- Tytuł:
- Kernels by Monochromatic Paths and Color-Perfect Digraphs
- Autorzy:
-
Galeana-Śanchez, Hortensia
Sánchez-López, Rocío - Powiązania:
- https://bibliotekanauki.pl/articles/31340961.pdf
- Data publikacji:
- 2016-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
kernel
kernel perfect digraph
kernel by monochromatic paths
color-class digraph
quasi color-perfect digraph
color-perfect digraph - Opis:
- For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no monochromatic directed path between them (N is mp-independent) and (2) for each vertex u in V (D) \ N there exists v ∈ N such that there is a monochromatic directed path from u to v in D (N is mp-absorbent). If every arc in D has a different color, then a kernel by monochromatic paths is said to be a kernel. Two associated digraphs to an arc-colored digraph are the closure and the color-class digraph C(D). In this paper we will approach an mp-kernel via the closure of induced subdigraphs of D which have the property of having few colors in their arcs with respect to D. We will introduce the concept of color-perfect digraph and we are going to prove that if D is an arc-colored digraph such that D is a quasi color-perfect digraph and C(D) is not strong, then D has an mp-kernel. Previous interesting results are generalized, as for example Richardson′s Theorem.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 309-321
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł