The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges
β Scribed by Eyal Ackerman, Noa Nitzan, Rom Pinchasi
- Book ID
- 120788870
- Publisher
- Springer Japan
- Year
- 2013
- Tongue
- English
- Weight
- 263 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Sanchis, L.A., Maximum number of edges in connected graphs with a given domination number, Discrete Mathematics 87 (1991) 65-72.
Suppose that n i> 2t + 2 (t/> 17). Let G be a graph with n vertices such that its complement is connected and, for all distinct non-adjacent vertices u and v, there are at least t common neighbours. Then we prove that and Furthermore, the results are sharp.
Let the reals be extended to include oo with o~ > r
A graph is 2K,-free if it does not contain an independent pair of edges as an induced subgraph. We show that if G is 2K,-free and has maximum degree A(G) = D, then G has at most 5D2/4 edges if D is even. If D is odd, this bound can be improved to (5D\* -20 + 1)/4. The extremal graphs are unique.