Improved upper bound on the Frank number of 3-edge-connected graphs

In an orientation O of the graph G, an arc e is deletable if and only if O-e is strongly connected. For a 3-edge-connected graph G, the Frank number is the minimum k for which G admits k strongly connected orientations such that for every edge e of G the corresponding arc is deletable in at least one of the k orientations. Horsch and Szigeti conjectured the Frank number is at most 3 for every 3-edge-connected graph G. We prove an upper bound of 5, which improves the previous bound of 7. (c) 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).