๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Planar k-cycle resonant graphs with k=1,2

โœ Scribed by Xiaofeng Guo; Fuji Zhang

Book ID
104294131
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
200 KB
Volume
129
Category
Article
ISSN
0166-218X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 1994. Some necessary and su cient conditions for a graph to be k-cycle resonant were also given. In this paper, we improve the proof of the necessary and su cient conditions for a graph to be k-cycle resonant, and further investigate planar k-cycle resonant graphs with k = 1; 2. Some new necessary and su cient conditions for a planar graph to be 1-cycle resonant and 2-cycle resonant are established.

๐Ÿ“œ SIMILAR VOLUMES

k-Cycle resonant graphs
k-Cycle resonant graphs
โœ Xiaofeng Guo; Fuji Zhang ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 492 KB

A connected graph G is said to be k-cycle resonant if, for 1 < t < 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. In this paper, we at the first time introduce the concept of k-cycle resonant

Graphs with k odd cycle lengths
Graphs with k odd cycle lengths
โœ A. Gyรกrfรกs ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 481 KB

Gyarf&, A., Graphs with k odd cycle lengths, Discrete Mathematics 103 (1992) 41-48. If G is a graph with k z 1 odd cycle lengths then each block of G is either KZk+2 or contains a vertex of degree at most 2k. As a consequence, the chromatic number of G is at most 2k + 2. For a graph G let L(G) deno