We show that for every ℓ , there exists d such 3-edge-connected graph with minimum degree can be edge-partitioned into paths of length (provided its number edges is divisible by ). This improves a result asserting 24-edge-connectivity and high provides partition. best possible as 3-edge-connectivity cannot replaced 2-edge connectivity.

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...