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.
Lower bounds on the number of edges in edge-chromatic-critical graphs with fixed maximum degrees
โ Scribed by Li, Xuechao; Wei, Bing
- Book ID
- 125801911
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 497 KB
- Volume
- 334
- Category
- Article
- ISSN
- 0012-365X
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## Abstract In 1968, Vizing [Uaspekhi Mat Nauk 23 (1968) 117โ134; Russian Math Surveys 23 (1968), 125โ142] conjectured that for any edge chromatic critical graph ${{G}} = ({{V}}, {{E}})$ with maximum degree $\Delta$, $|{{E}}| \geq {{{1}}\over {{2}}}\{(\Delta {{- 1}})|{{V}}| + {{3}}\}$. This conject
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