Edge-colored complete graphs with precisely colored subgraphs
β Scribed by F. R. K. Chung; R. L. Graham
- Book ID
- 110564237
- Publisher
- Springer-Verlag
- Year
- 1983
- Tongue
- English
- Weight
- 431 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
It is shown that, for β ) 0 and n ) n β , any complete graph K on n vertices 0 ' Ε½ . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y β n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and
We prove that if the edges of the complete graph on n ~4 vertices are colored so that no vertex is on more than A edges of the same color, 1 c A < n -2,, then the graph has cycles of all lengths 3 through n with no A consecutive edges the same color.
## Abstract An edgeβcolored graph __H__ is properly colored if no two adjacent edges of __H__ have the same color. In 1997, J. BangβJensen and G. Gutin conjectured that an edgeβcolored complete graph __G__ has a properly colored Hamilton path if and only if __G__ has a spanning subgraph consisting