✦ LIBER ✦

Tree decomposition of graphs

✍ Scribed by Raphael Yuster

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 207 KB
Volume: 12
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199805)12:3<237::aid-rsa2>3.0.co;2-w

No coin nor oath required. For personal study only.

✦ Synopsis

with ␦ G G V r2 q 10 h V log V , and h y 1 divides E , then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.

📜 SIMILAR VOLUMES

P4-decompositions of regular graphs

✍ Heinrich, Katherine; Liu, Jiping; Yu, Minli 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 246 KB 👁 1 views

In this article, we show that every simple r-regular graph G admits a balanced P 4 -decomposition if r ≡ 0(mod 3) and G has no cut-edge when r is odd. We also show that a connected 4-regular graph G admits a P 4 -decomposition if and only if |E(G)| ≡ 0(mod 3) by characterizing graphs of maximum degr

Metric characterizations of proper inter

Metric characterizations of proper interval graphs and tree-clique graphs

✍ Gutierrez, M.; Oubi�a, L. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 393 KB 👁 1 views

A connected graph G is a tree-clique graph if there exists a spanning tree T (a compatible tree) such that every clique of G is a subtree of T. When Tis a path the connected graph G is a proper interval graph which is usually defined as intersection graph of a family of closed intervals of the real

Graphs omitting a bushy tree

✍ Cherlin, G.; Shi, N.; Tallgren, L. 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 152 KB 👁 1 views

A tree is called bushy if it has no vertex of degree 2. Theorem: the class of countable graphs omitting a fixed finite bushy tree with at least 5 vertices has no universal element.

Random trees and random graphs

✍ Tomasz Łuczak 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 205 KB 👁 2 views

In the paper we study the asymptotic behavior of the number of trees with n Ž . Ž . vertices and diameter k s k n , where n y k rnª a as n ª ϱ for some constant a-1. We use this result to determine the limit distribution of the diameter of the random graph Ž .

Graph decompositions without isolated ve

Graph decompositions without isolated vertices III

✍ Enomoto, Hikoe; Matsunaga, Shinsuke 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 135 KB

Let G be a graph of order n, and n = k i=1 a i be a partition of n with a i ≥ 2. In this article we show that if the minimum degree of G is at least 3k -2, then for any distinct and ``the subgraph induced by A i contains no isolated vertices'' for all i, 1 ≤ i ≤ k. Here, the bound on the minimum de

r-Regular, r-connected decompositions of

r-Regular, r-connected decompositions of complete graphs

✍ H. Fleischner; W. R. Johnstone; A. J. W. Hilton 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 139 KB

If rjn À 1 and rn is even, then K n can be expressed as the union of t nÀ1 r edgedisjoint isomorphic r-regular r-connected factors.