Suppose G is a graph of n vertices and diameter at most d having the property that, after deleting any vertex, the resulting subgraph has diameter at most 6. Then G contains at least max{n. r(4n -8)/31} edges if 4 s d s 6 . ## 1. Introduction We consider finite undirected simple graphs. (Terminolo
Extremal graphs of diameter 4
β Scribed by L Caccetta
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 555 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
It is known that for each d there exists a graph of diameter two and maximum degree d which has at least (d/2) (d + 2)/2 vertices. In contrast with this, we prove that for every surface S there is a constant d S such that each graph of diameter two and maximum degree d β₯ d S , which is embeddable in
## Abstract We shall prove that if __L__ is a 3βchromatic (so called βforbiddenβ) graph, and β__R__^__n__^ is a random graph on __n__ vertices, whose edges are chosen independently, with probability __p__, and β__B__^__n__^ is a bipartite subgraph of __R__^__n__^ of maximum size, β__F__^__n__^ is a