We show that the edges of a 2-connected graph can be partitioned into two color classes so that every vertex is incident with edges of each color and every alternating cycle passes through a single edge. We also show that the edges of a simple graph with minimum vertex degree 6 2 2 can be partitione
The heterochromatic cycles in edge-colored graphs
โ Scribed by Dongxiao Yu; Guizhen Liu; Shuo Li
- Publisher
- Springer-Verlag
- Year
- 2008
- Tongue
- English
- Weight
- 291 KB
- Volume
- 30
- Category
- Article
- ISSN
- 1598-5865
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It is shown that, for โ ) 0 and n ) n โ , any complete graph K on n vertices 0 ' ลฝ . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y โ 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.