## Abstract Ore derived a sufficient condition for a graph to contain a Hamiltonian cycle. We obtain a sufficient condition, similar to Ore's condition, for a graph to contain a Hamiltonian cycle and a 1‐factor which are edge disjoint.
A sufficient degree condition for a graph to contain all trees of sizek
✍ Scribed by Camino Balbuena; Alberto Márquez; José Ramón Portillo
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2010
- Tongue
- English
- Weight
- 174 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Let __G__ be a connected graph of order __p__ ≥ 2, with edge‐connectivity κ~1~(__G__) and minimum degree δ(__G__). It is shown her ethat in order to obtain the equality κ~1~(__G__) = δ(__G__), it is sufficient that, for each vertex __x__ of minimum degree in __G__, the vertices in the n
## Abstract The core __G__Δ of a simple graph __G__ is the subgraph induced by the vertices of maximum degree. It is well known that the Petersen graph is not 1‐factorizable and has property that the core of the graph obtained from it by removing one vertex has maximum degree 2. In this paper, we p