Even cycle decompositions of 4-regular graphs and line graphs
✍ Scribed by Klas Markström
- Book ID
- 113567545
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 367 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
In this article, we show that every simple r-regular graph G admits a balanced P 4 -decomposition if r ≡ 0(mod 3) and G has no cut-edge when r is odd. We also show that a connected 4-regular graph G admits a P 4 -decomposition if and only if |E(G)| ≡ 0(mod 3) by characterizing graphs of maximum degr
## Abstract A transition system __T__ of an Eulerian graph __G__ is a family of partitions of the edges incident to each vertex of __G__ into transitions, that is, subsets of size two. A circuit decomposition $\cal C$ of __G__ is compatible with __T__ if no pair of adjacent edges of __G__ is both a
## Abstract In 1960, Dirac posed the conjecture that __r__‐connected 4‐critical graphs exist for every __r__ ≥ 3. In 1989, Erdős conjectured that for every __r__ ≥ 3 there exist __r__‐regular 4‐critical graphs. In this paper, a technique of constructing __r__‐regular __r__‐connected vertex‐transiti
## Abstract Kotzig asked in 1979 what are necessary and sufficient conditions for a __d__‐regular simple graph to admit a decomposition into paths of length __d__ for odd __d__>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable
Some sufficient conditions are proven for the complete graph of even order with a 1-factor removed to be decomposable into even length cycles. 0 1994 John Wiley & Sons, Inc. ## 1. Introduction It is natural to ask when a complete graph admits a decomposition into cycles of some fixed length. Since