Circumference and girth
β Scribed by Cun-Quan Zhang
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 257 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Let G be 2-connected graph with girth g and minimum degree d. Then each, pair of verticfs of G is joined by a path of length a t least maxi? (dl)g, ( d -?) (g -4) + 2) if g B 4, and the length of a longest cycle of G is at least max{[(d -1) (g -2) + 21, [(2d -3) (g -4) + 41).
π SIMILAR VOLUMES
In this paper, the lower bounds of maximum genera of simplicial graphs under the constraints of girth and connectivity are discussed extensively. A complete picture on the lower bounds of maximum genera of graphs is formed. There are infinitely many graphs with the maximum genera attaining these low
## Abstract For an integer __k__ > 2, the best function __m__(__n, k__) is determined such that every strong digraph of order __n__ with at least __m__(__n, k__) arcs contains a circuit of length __k__ or less.
## Abstract We prove that every graph of circumference __k__ has treeβwidth at most __k__βββ1 and that this bound is best possible. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 43: 24β25, 2003
We prove several tight lower bounds in terms of the order and the average degree for the independence number of graphs that are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle-free graphs of maximum degree a