This document presents a class of Minimum Cost Blocking problems in Wireless Mesh Networks that use multi-path wireless routing protocols. It establishes that multi-path routing protocols are superior to conventional single-path protocols in resisting blocking, node isolation, and network partitioning attacks. It analyzes two scenarios - one with low network node mobility and one with high mobility - and proves the problems are NP-hard and #P-hard, respectively, for adversaries. It also provides approximation algorithms and simulations showing multi-path protocols are exponentially harder for adversaries to optimally attack.