𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the homogeneous algebraic graphs of large girth and their applications

✍ Scribed by T. Shaska; V. Ustimenko


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
179 KB
Volume
430
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


On the bipartite density of regular grap
✍ OndΕ™ej ZΓ½ka πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 154 KB πŸ‘ 1 views

## Abstract Let __B(G)__ be the edge set of a bipartite subgraph of a graph __G__ with the maximum number of edges. Let __b~k~__ = inf{|__B(G)__|/|__E(G)__β€–__G__ is a cubic graph with girth at least __k__}. We will prove that lim~k β†’ ∞~ __b~k~__ β‰₯ 6/7.

The circular chromatic number of series-
✍ Chien, Chihyun; Zhu, Xuding πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 213 KB πŸ‘ 2 views

It was proved by Hell and Zhu that, if G is a series-parallel graph of girth at least 2 (3k -1)/2 , then Ο‡ c (G) ≀ 4k/(2k -1). In this article, we prove that the girth requirement is sharp, i.e., for any k β‰₯ 2, there is a series-parallel graph G of girth 2 (3k -1)/2 -1 such that Ο‡ c (G) > 4k/(2k -1)

On the girth of hamiltonian weakly pancy
✍ BollobοΏ½s, BοΏ½la; Thomason, Andrew πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 130 KB πŸ‘ 2 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 ErdΕ‘s, 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 smallest graphs of girth 10 and v
✍ P.K. Wong πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 511 KB

Recently, O'Keefe and Wong have shown that a smallest graph of girth 10 and valency 3 (a (3,lO)-cage) must have 70 vertices. There are three non-isomorphic (3,10)-cages which have been known for some while. In this papel, it is shown that these are the only three possible (3,lO)-cages. Some of the p

On the structure of extremal graphs of h
✍ Lazebnik, Felix; Wang, Ping πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 117 KB πŸ‘ 2 views

Let n β‰₯ 3 be a positive integer, and let G be a simple graph of order v containing no cycles of length smaller than n + 1 and having the greatest possible number of edges (an extremal graph). Does G contain an n + 1-cycle? In this paper we establish some properties of extremal graphs and present sev