3 problems

Mader's nonseparating dipath conjecture. If

A digraph is $p$-strongly connected when its strong connectivity is at least $p$. Lovász's conjecture. There exists an integer $p$ such that every $p$-strongly connected digraph ha…

Let an $\ell$-word be a word of length $\ell$ over an $n$-letter alphabet, and suppose it has a unique factorisation into factors corresponding to alphabet-disjoint partitions. A w…