Let G and K be connected graphs such that I GI = nlKl (n 2 2) and let p be a fixed integer satisfying 1 < p < n. We prove that if G \ A has a K-factor for every connected subgraph A with IAl = plKI, then G also has a K-factor.
Factors and Connected Induced Subgraphs
β Scribed by Keiko Kotani
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 83 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We give an upper bound for w(A), the minimum cyclomatic number of connected induced subgraphs containing a given independent set A of vertices in a given graph G. We also give an upper bound for w(A) when G is triangle-free. We show that these two bounds are best possible. Similar results are obtai
## Abstract A theorem of Mader states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. We extend this result to infinite graphs. Here, it is necessary to require not only high degree for the vertices but also high __vertexβdegree__ (or __multiplicity
## Abstract For a graph __G__ we define a graph __T__(__G__) whose vertices are the triangles in __G__ and two vertices of __T__(__G__) are adjacent if their corresponding triangles in __G__ share an edge. Kawarabayashi showed that if __G__ is a __k__βconnected graph and __T__(__G__) contains no ed