On 4--critical graphs of diameter two
β Scribed by Wang, Yan; Wang, Chunxiang
- Book ID
- 122419257
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 865 KB
- Volume
- 161
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
A graph is diameter 2-critical if the graph has diameter 2 and the deletion of any edge increases its diameter. We prove that if G is diameter 2-critical graph on n vertices and e edges, then (i) e ~< [14n2 ] for n <~ 24, and (ii) e < !4n2 + (n 2 -16.2 n + 56)/320 (<0.2532 n2), for n/> 25.
A graph is vertex-critical if deleting any vertex increases its diameter. We construct, for each & 5 except &=6, a vertex-critical graph of diameter two on & vertices with at least , where c 2 is some constant. We also construct, for each & 5 except &=6, a vertex-critical graph of diameter two on &