Monochromatic paths in edge-colored graphs
✍ Scribed by V Chvátal
- Publisher
- Elsevier Science
- Year
- 1972
- Tongue
- English
- Weight
- 64 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0095-8956
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In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G) = . Generalizing a classical conjecture of Erd" os, Gyárfás and Pyber, we conjecture that if we r-color the edges of a graph G with (G) = , then the ver
## 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 Sufficient degree conditions for the existence of properly edge‐colored cycles and paths in edge‐colored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edge‐colored multigraph of order __n__ on at least three colors and with minimum colored degre