## Abstract The odd girth of a graph __G__ gives the length of a shortest odd cycle in __G.__ Let __f(k,g)__ denote the smallest __n__ such that there exists a __k__βregular graph of order __n__ and odd girth __g.__ The exact values of __f(k,g)__ are determined if one of the following holds: __k__
Graphs of Prescribed Girth and Bi-Degree
β Scribed by Z. Furedi; F. Lazebnik; A. Seress; V.A. Ustimenko; A.J. Woldar
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 426 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The degree set π^G^ of a graph __G__ is the set of degrees of the vertices of __G.__ For a finite nonempty set __S__ of positive integers, all positive integers __p__ are determined for which there exists a graph __G__ of order __p__ such that π^G^ = __S__.
## Abstract It is well known that certain graphβtheoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (__p__, Ξ, Ξ΄, Ξ») graph as a graph having __p__ points,
## Abstract For each fixed __k__ββ₯β0, we give an upper bound for the girth of a graph of order __n__ and size __n__β+β__k__. This bound is likely to be essentially best possible as __n__ββββ. Β© 2002 Wiley Periodicals, Inc. J Graph Theory 39: 194β200, 2002; DOI 10.1002/jgt.10023
We prove that the vertex set of a simple graph with minimum degree at least s + t -1 and girth at least 5 can be decomposed into two parts, which induce subgraphs with minimum degree at least s and t, respectively, where s, t are positive integers β₯ 2.
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