## 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 β~ __b~k~__ β₯ 6/7.
The Size of Bipartite Graphs with a Given Girth
β Scribed by Shlomo Hoory
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 90 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair was proved by Harary and KovΓ‘cs [Regular graphs with given girth pair, J Graph Theory 7 (1983), 209β218]. A (Ξ΄, __g__)βcage is a small
## Abstract The odd girth of a graph __G__ is the length of a shortest odd cycle in __G__. Let __d__(__n, g__) denote the largest __k__ such that there exists a __k__βregular graph of order __n__ and odd girth __g__. It is shown that __d____n, g__ β₯ 2|__n__/__g__β₯ if __n__ β₯ 2__g__. As a consequenc
d 2,n 2 ) is a bipartite graphical sequence, if there is a bipartite graph G with degrees {D 1 , D 2 } (i.e., G has two independent vertex sets In other words, {D 1 , D 2 } is a bipartite graphical sequence if and only if there is an n 1 1 n 2 matrix of 0's and 1's having d 1j 1 1's in row j 1 and