## Abstract A graph __g__ of diameter 2 is minimal if the deletion of any edge increases its diameter. Here the following conjecture of Murty and Simon is proved for __n__ < __n__~o~. If __g__ has __n__ vertices then it has at most __n__^2^/4 edges. The only extremum is the complete bipartite graph
The number of edges in a maximum cycle—distributed graph
✍ Scribed by Yongbing Shi
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 288 KB
- Volume
- 104
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
Shi, Y., The number of edges in a maximum cycle-distributed graph, Discrete Mathematics 104 (1992) 205-209. Let f(n) (f*(n)) be the maximum possible number of edges in a graph (2-connected simple graph) on n vertices in which no two cycles prove that, for every integer n > 3, f(n) 3 n + k + [i( [~(sG=z + ll)], and obtain upper and lower bounds on fi(n).
📜 SIMILAR VOLUMES
## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__ = __q__ − __p__ = 1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__ − 1^ = __o__(2^__r__ − 1^) cycles. The planar result is best possib
Sanchis, L.A., Maximum number of edges in connected graphs with a given domination number, Discrete Mathematics 87 (1991) 65-72.
Let G=(V 1 , V 2 ; E ) be a bipartite graph with |V 1 |= |V 2 | =n 2k, where k is a positive integer. Suppose that the minimum degree of G is at least k+1. We show that if n>2k, then G contains k vertex-disjoint cycles. We also show that if n=2k, then G contains k&1 quadrilaterals and a path of orde
Let the reals be extended to include oo with o~ > r
Soit H = (X. ~1 un hypergraphe h-uniforme avec IX] = net soit L h ~(H! le graphe Jont les sommets reprdsentent les arates de H, deux sommets 6lant reli6s si et seulement si t~s z~r6tes qu'ils reprdsen!ent intersectent en h -1 sommet,=. Nous montrons que sif,, t(H) ne contienl pas de cycle, alors I~[