Toughness of Graphs and [2,b]-Factors
β Scribed by Ciping Chen
- Publisher
- Springer Japan
- Year
- 1994
- Tongue
- English
- Weight
- 132 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## Theorem 2. Let G be a 2-tough graph. Then for any function f : V(G)+ { 1, 2) such that C xsvCcj f (x) in euen, G has an f-factor. Before stating the second main theorem of this paper it is necessary to make the following definition. Let G be a graph and let g and f be two integer-valued functi
For integers a and b such that 0~ Q < b, a graph G is called an [a, b]-graph if a s c&(x) s b for every vertex x of G and a factor F of a graph is called an [a, b]-factor if a s d&) i b for every vertex x of F. We prove the following theorems. Let 0 c 1 d k s r, 0 s s, 0 G u and 1 d t. Then an [r, r
Let G be a planar graph on n vertices, let c(G) denote the length of a longest cycle of G, and let w(G) denote the number of components of G. By a well-known theorem of Tutte, c(G) = n (i.e., G is hamiltonian) if G is 4-connected. Recently, Jackson and Wormald showed that c(G) 2 ona for some positiv