Upper bound to the number of edges of a graph with specified nondensity and all-contiguity numbers
โ Scribed by N. G. Vinnichenko
- Book ID
- 105057170
- Publisher
- Springer US
- Year
- 1974
- Tongue
- English
- Weight
- 157 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1573-8337
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let G be a connected and simple graph, and let i(G) denote the number of stable sets in G. In this letter, we have presented a sharp upper bound for the i(G)-value among the set of graphs with k cut edges for all possible values of k, and characterized the corresponding extremal graphs as well.
In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) โค n / 2, where (G) is the independence number of G. In this paper, we apply Vizing and Vizing-like adjacency lemmas to this problem and prove that (G)<(((5 -6)n) / (8 -6))<5n / 8 if โฅ 6. แญง 2010 Wiley
In this paper, we prove that any edge-coloring critical graph G with maximum degree ยฟ (11 + โ 49 -24 )=2, where 6 1, has the size at least 3(|V (G)| -) + 1 if 6 7 or if ยฟ 8 and |V (G)| ยฟ 2 --4 -( + 6)=( -6), where is the minimum degree of G. It generalizes a result of Sanders and Zhao.