Path partitions and Pn-free sets

The detour order@t(G) of a graph G is the order of a longest path of G. If S is a subset of V(G) such that the graph induced by S has detour order at most n, then S is called a P"n"+"1-free set in G. The Path Partition Conjecture (PPC) can be stated as follows: For any graph G and any positive integer n<@t(G),there exists a P"n"+"1-free set H in G such that @t(G-H)=<@t(G)-n. We prove that if G is any graph and M is any maximal P"n"+"1-free set in G, then @t(G-M)=<@t(G)-23(n+1). We also prove that if G has no cycle of order less than n or greater than @t(G)-n+2, then @t(G-M)=<@t(G)-n for every maximal P"n"+"1-free subset M of G. As a corollary of the latter result we prove that the PPC is true for the class of connected, weakly pancyclic graphs.