- Tytuł:
- Stronger bounds for generalized degrees and Menger path systems
- Autorzy:
-
Faudree, R.
Tuza, Zs. - Powiązania:
- https://bibliotekanauki.pl/articles/972047.pdf
- Data publikacji:
- 1995
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
generalized degree
Menger - Opis:
- For positive integers d and m, let $P_{d,m}(G)$ denote the property that between each pair of vertices of the graph G, there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δₜ(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree conditions that ensure that $P_{d,m}(G)$ is satisfied have been investigated. In particular, it has been shown, for fixed positive integers t ≥ 5, d ≥ 5t², and m, that if an m-connected graph G of order n satisfies the generalized degree condition δₜ(G) > (t/(t+1))(5n/(d+2))+(m-1)d+3t², then for n sufficiently large G has property $P_{d,m}(G)$. In this note, this result will be improved by obtaining corresponding results on property $P_{d,m}(G)$ using a generalized degree condition δₜ(G), except that the restriction d ≥ 5t² will be replaced by the weaker restriction d ≥ max{5t+28,t+77}. Also, it will be shown, just as in the original result, that if the order of magnitude of δₜ(G) is decreased, then $P_{d,m}(G)$ will not, in general, hold; so the result is sharp in terms of the order of magnitude of δₜ(G).
- Źródło:
-
Discussiones Mathematicae Graph Theory; 1995, 15, 2; 167-177
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł