- Tytuł:
- An implicit weighted degree condition for heavy cycles
- Autorzy:
-
Cai, Junqing
Li, Hao
Ning, Wantao - Powiązania:
- https://bibliotekanauki.pl/articles/30148719.pdf
- Data publikacji:
- 2014-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
weighted graph
hamiltonian cycles
heavy cycles
implicit degree
implicit weighted degree - Opis:
- For a vertex v in a weighted graph G, idw(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy /∈ E(G); (c) In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a hamiltonian cycle or a cycle of weight at least 2t/3. This generalizes the result of Zhang et al. [9].
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2014, 34, 4; 801-810
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł