Properly colored cycles in edge-colored graphs are closely related to directed oriented graphs. As an analogy of the well-known Caccetta–Häggkvist Conjecture, we study existence properly bounded length graph. We first prove that for all integers s and t with ≥ 2 , every graph G no K contains a spanning subgraph H which admits orientation D such cycle is . Using this result, show r 4 if Conjectu...

The study of problems modeled by edge-colored graphs has given rise to important developments during the last few decades. For instance, the investigation of spanning trees for graphs provide important and interesting results both from a mathematical and an algorithmic point of view (see for instance [1]). From the point of view of applicability, problems arising in molecular biology are often ...