PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Discussiones Mathematicae Graph Theory

2011 | 31 | 1 | 143-159
Tytuł artykułu

### Closure for spanning trees and distant area

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with $deg_G u + deg_G v ≥ n-1$, G has a spanning k-ended tree if and only if G+uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. We investigate the relationship between the condition on $deg_G u + deg_G v$ and the structure of the distant area for u and v. We prove that if the distant area contains $K_r$, we can relax the lower bound of $deg_G u + deg_G v$ from n-1 to n-r. And if the distant area itself is a complete graph and G is 2-connected, we can entirely remove the degree sum condition.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
143-159
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-09-29
zaakceptowano
2010-04-19
Twórcy
autor
• Department of Applied Science, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan
autor
• Department of Computer Science, Nihon University, Sakurajosui 3-25-40, Setagaya-Ku, Tokyo 156-8550, Japan
autor
• Institut für Diskrete Mathematik und Algebra, Technische Universität, Bergakademie Freiberg, D-09596 Freiberg, Germany
Bibliografia
• [1] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135, doi: 10.1016/0012-365X(76)90078-9.
• [2] H.J. Broersma and I. Schiermeyer, A closure concept based on neighborhood unions of independent triples, Discrete Math. 124 (1994) 37-47, doi: 10.1016/0012-365X(92)00049-W.
• [3] H. Broersma and H. Tuinstra, Independence trees and Hamilton cycles, J. Graph Theory 29 (1998) 227-237, doi: 10.1002/(SICI)1097-0118(199812)29:4<227::AID-JGT2>3.0.CO;2-W
• [4] G. Chartrand and L. Lesniak, Graphs & Digraphs (4th ed.), (Chapman and Hall/CRC, Boca Raton, Florida, U.S.A. 2005).
• [5] Y.J. Zhu, F. Tian and X.T. Deng, Further consideration on the Bondy-Chvátal closure theorems, in: Graph Theory, Combinatorics, Algorithms, and Applications (San Francisco, CA, 1989), 518-524.
Typ dokumentu
Bibliografia
Identyfikatory