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The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges

✍ 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

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πŸ“œ SIMILAR VOLUMES


The maximum number of edges in a graph w
✍ R.J. Faudree; J. Sheehan πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 633 KB

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.

The maximum number of edges in 2K2-free
✍ F.R.K. Chung; A. GyΓ‘rfΓ‘s; Z. Tuza; W.T. Trotter πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 481 KB

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.