Decompositions of highly connected graphs into paths of length 3

Abstract

Abstract We prove that a 171‐edge‐connected graph has an edge‐decomposition into paths of length 3 if and only its size is divisible by 3. It is a long‐standing problem whether 2‐edge‐connectedness is sufficient for planar triangle‐free graphs, and whether 3‐edge‐connectedness suffices for graphs in general. © 2008 Wiley Periodicals, Inc. J Graph Theory 58: 286–292, 2008