We prove the following property for safe marked graphs, safe conflict-free Petri nets, and live and safe extended free-choice Petri nets. We prove the following three results. If the Petri net is a marked graph, then the length of the shortest path is at most ( | T | − 1 ) ⋅ | T | / 2 . If the Petri net is conflict free, then the length of the shortest path is at most ( | T | + 1 ) ⋅ | T | / 2 . If the petrinet is live and extended free choice, then the length of the shortest path is at most | T | ⋅ | T + 1 | ⋅ | T + 2 | / 6 , where T is the set of transitions of the net.