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.
Edge-colored graphs with applications to homogeneous faults
β Scribed by Yongge Wang; Yvo Desmedt
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 236 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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
## This paper is complementary to Kubale (1989). We consider herein a problem of interval coloring the edges of a graph under the restriction that certain colors cannot be used for some edges. We give lower and upper bounds on the minimum number of colors required for such a coloring. Since the ge