## Abstract Chvátal and Erdös showed that a __k__‐connected graph with independence number at most __k__ and order at least three is hamiltonian. In this paper, we show that a graph contains a 2‐factor with two components, i.e., the graph can be divided into two cycles if the graph is __k__(≥ 4)‐co
A chvátal–erdős type condition for hamiltonian graphs
✍ Scribed by Xiaoyun Lu
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 443 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0364-9024
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📜 SIMILAR VOLUMES
## Abstract Let __G__ be a 2‐connected graph of order __n.__ We show that if for each pair of nonadjacent vertices __x__,__y__ ∈ __V(G)__, then __G__ is Hamiltonian.
## Abstract In this paper, we show that __n__ ⩾ 4 and if __G__ is a 2‐connected graph with 2__n__ or 2__n__−1 vertices which is regular of degree __n__−2, then __G__ is Hamiltonian if and only if __G__ is not the Petersen graph.
The total chromatic number χ T (G) of graph G is the least number of colors assigned to V (G) ∪ E(G) such that no adjacent or incident elements receive the same color. In this article, we give a sufficient condition for a bipartite graph G to have χ T (G) = ∆(G) + 1.
For an integer i, a graph is called an L,-graph if, for each triple of vertices u, u , w with and Khachatrian proved that connected Lo-graphs of order a t least 3 are hamiltonian, thus improving Ore's Theorem. All K1,3-free graphs are L1-graphs, whence recognizing hamiltonian L1-graphs is an NP-com