A connected graph is said to be k-cycle resonant if, for 1 6 t 6 k, any t disjoint cycles in G are mutually resonant, that is, there is a perfect matching M of G such that each of the t cycles is an M -alternating cycle. The concept of k-cycle resonant graphs was introduced by the present authors in
Reducible chains of planar 1-cycle resonant graphs
β Scribed by Xiaofeng Guo; Fuji Zhang
- Book ID
- 108315886
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 387 KB
- Volume
- 275
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Zhang, F. and X. Guo, Reducible chains in several types of 2-connected graphs, Discrete Mathematics 105 (1992) 285-291. Let F& 4, $ and 8 denote the sets of all 2-connected graphs, minimally 2-connected graphs, critically 2-connected graphs, and critically and minimally 2-connected graphs, respecti
It is easy to see that planar graphs without 3-cycles are 3-degenerate. Recently, it was proved that planar graphs without 5-cycles are also 3-degenerate. In this paper it is shown, more surprisingly, that the same holds for planar graphs without 6-cycles.