✦ LIBER ✦

Various results on the toughness of graphs

✍ Scribed by Broersma, Hajo; Engbers, Erik; Trommel, Huib

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 90 KB
Volume: 33
Category: Article
ISSN: 0028-3045
DOI: 10.1002/(sici)1097-0037(199905)33:3<233::aid-net9>3.0.co;2-a

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a graph and let t Ն 0 be a real number. Then,

We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sufficient degree conditions implying that (G) Ն t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.

📜 SIMILAR VOLUMES

On the Fracture Toughness of Advanced Ma

On the Fracture Toughness of Advanced Materials

✍ Maximilien E. Launey; Robert O. Ritchie 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 340 KB 👁 1 views

## Abstract Few engineering materials are limited by their strength; rather they are limited by their resistance to fracture or fracture toughness. It is not by accident that most critical structures, such as bridges, ships, nuclear pressure vessels and so forth, are manufactured from materials tha

On the linear arboricity of planar graph

On the linear arboricity of planar graphs

✍ Wu, Jian-Liang 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB 👁 2 views

The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree ∆. The conjecture has been proved to be true for graphs having ∆ =

On the chromatic number of disk graphs

✍ Malesi?ska, Ewa; Piskorz, Steffen; Wei�enfels, Gerhard 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 172 KB 👁 2 views

Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their

On the existence of countable universal

On the existence of countable universal graphs

✍ F�redi, Zolt�n; Komj�th, P�ter 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB 👁 1 views

Let Forb(G) denote the class of graphs with countable vertex sets which do not contain G as a subgraph. If G is finite, 2-connected, but not complete, then Forb(G) has no element which contains every other element of Forb(G) as a subgraph, i.e., this class contains no universal graph.

On the girth of hamiltonian weakly pancy

On the girth of hamiltonian weakly pancyclic graphs

✍ Bollob�s, B�la; Thomason, Andrew 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 130 KB 👁 1 views

A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In answer to a question of Erdős, we show that a Hamiltonian weakly-pancyclic graph of order n can have girth as large as about 2 n/ log n. In contrast to this, we show that the existence of

On the second largest eigenvalue of line

On the second largest eigenvalue of line graphs

✍ Petrovi?, Miroslav; Mileki?, Bojana 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 169 KB 👁 2 views

In this paper all connected line graphs whose second largest eigenvalue does not exceed 1 are characterized. Besides, all minimal line graphs with second largest eigenvalue greater than 1 are determined.