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Nowhere-zero $3$-flows in Cayley graphs on solvable groups of twice square-free order
We verify Tutte's $3$-flow conjecture in the class of Cayley graphs on solvable groups of order $2n$, where $n$ is square-free. The proof relies on a new necessary and sufficient condition for a simple $5$-valent graph to admit a nowhere-zero $3$-flow in terms of a special pseudoforest decomposition
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