It is shown that, for ⑀ ) 0 and n ) n ⑀ , any complete graph K on n vertices 0 ' Ž . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y ⑀ n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and
Existence of rainbow matchings in properly edge-colored graphs
✍ Scribed by Guanghui Wang; Jianghua Zhang; Guizhen Liu
- Book ID
- 113083694
- Publisher
- Higher Education Press and Springer
- Year
- 2012
- Tongue
- English
- Weight
- 99 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1673-3452
No coin nor oath required. For personal study only.
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## Abstract An edge‐colored graph __H__ is properly colored if no two adjacent edges of __H__ have the same color. In 1997, J. Bang‐Jensen and G. Gutin conjectured that an edge‐colored complete graph __G__ has a properly colored Hamilton path if and only if __G__ has a spanning subgraph consisting
## Abstract A face of an edge‐colored plane graph is called __rainbow__ if the number of colors used on its edges is equal to its size. The maximum number of colors used in an edge coloring of a connected plane graph __G__with no rainbow face is called __the edge‐rainbowness__ of __G__. In this pap
Given a graph G and a subgraph H of G, let rb(G, H) be the minimum number r for which any edge-coloring of G with r colors has a rainbow subgraph H. The number rb(G, H) is called the rainbow number of H with respect to G. Denote as mK 2 a matching of size m and as B n,k the set of all the k-regular