## 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
Maximum Genus, Girth and Connectivity
β Scribed by Deming Li; Yanpei Liu
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 88 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
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 lower bounds.
π SIMILAR VOLUMES
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga
This paper shows that a simple graph which can be cellularly embedded on some closed surface in such a way that the size of each face does not exceed 7 is upper embeddable. This settles one of two conjectures posed by Nedela and S8 koviera (1990, in ``Topics in Combinatorics and Graph Theory,'' pp.
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