Properly Colored Paths and Cycles
Discrete Applied Mathematics
In an edge-colored graph, let dc(v) be the number of colors on the edges incident to v and let δc(G) be the minimum dc(v) over all vertices v∈G. In this work, we consider sharp conditions on δc(G) which imply the existence of properly edge-colored paths and cycles, meaning no two consecutive edges have the same color.
Fujita, Shinya, Colton Magnant.
"Properly Colored Paths and Cycles."
Discrete Applied Mathematics, 159 (14): 1391-1397.