✦ LIBER ✦

The number of trees with a 1-factor

✍ Scribed by J.W. Moon

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 608 KB
Volume: 63
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90149-x

No coin nor oath required. For personal study only.

✦ Synopsis

The asymptotic behaviour of the number of trees with a 1-factor is determined for various families of trees

📜 SIMILAR VOLUMES

Trees with 1-factors and oriented trees

✍ Rodica Simion 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 632 KB

Simion, R., Trees with l-factors and oriented trees, Discrete Mathematics 88 (1991) 93-104. In this paper we present some results on trees with a l-factor: generating functions and asymptotics for the number of such trees, labeled, rooted, planted and unlabeled. We show that almost all trees with a

Trees with the minimum Wiener number

✍ Shu-Chung Liu; Li-Da Tong; Yeong-Nan Yeh 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 283 KB

The Wiener number (W) of a connected graph is the sum of distances for all pairs of vertices. As a graphical invariant, it has been found extensive application in chemistry. Considering the family of trees with n vertices and a fixed maximum vertex degree, we derive some methods that can strictly re

Trees Associated with the Motzkin Number

Trees Associated with the Motzkin Numbers

✍ Alexander Kuznetsov; Igor Pak; Alexander Postnikov 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 179 KB

We consider plane rooted trees on n+1 vertices without branching points on odd levels. The number of such trees in equal to the Motzkin number M n . We give a bijective proof of this statement.

Graphs with an extremal number of spanni

Graphs with an extremal number of spanning trees

✍ A. K. Kelmans 📂 Article 📅 1980 🏛 John Wiley and Sons 🌐 English ⚖ 129 KB 👁 1 views

On the Ramsey number of trees versus gra

On the Ramsey number of trees versus graphs with large clique number

✍ Ronald J. Gould; Michael S. Jacobson 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 335 KB

Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3

On graphs with the maximum number of spa

On graphs with the maximum number of spanning trees

✍ Alexander K. Kelmans 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 814 KB

Let 3:; denote the set of simple graphs with n vertices and m edges, t ( G ) the number of spanning trees of a graph G , and F 2 H if t(K,\E(F))?t(K,\E(H)) for every s? max{u(F), u ( H ) } . We give a complete characterization of >-maximal (maximum) graphs in 3:; subject to m 5 n . This result conta