Properly colored paths and cycles
In an edge-colored graph, let dc(v) d c ( v ) be the number of colors on the edges incident to v v and let ?c(G) ? c ( G ) be the minimum dc(v) d c ( v ) over all vertices v?G v ? G . In this work, we consider sharp conditions on ?c(G) ? c ( G ) which imply the existence of properly edge-colored paths and cycles, meaning no two consecutive edges have the same color.
properly colored paths edge-colored graphs properly colored cycles