Mutually exclusive replacement paths, an existing problem?
I found a replacement path allocation for $_$ in a more general setting. Consider an edge $_1$ that uses edge $_2$ on its path. The allocation induces a dependency from $_1$ to $_2$. Mutual exclusion defined above corresponds to a cycle of 2 such dependencies. Now consider the more general setting: a cycle of $$ dependencies induced by a path allocation on $_$. Assume vertices are $0,…,−1$. On edges $,$, the path allocation $,+1,0,+1,$ induces cycles of dependencies no shorter than $$. In my application it means that $_$ can tolerate up to $−1$ edge failures (i.e. edge removal).

Same problem on hypercubes, published here:
''Local Fast Segment Rerouting on Hypercubes''

Further solutions were submitted recently. Will update soon.