Tutte's 3-flow conjecture asserts that every 4-edge-connected graph admits a nowhere-zero 3-flow. We prove that this conjecture is true for every Cayley graph of valency at least four on any supersolvable group with a noncyclic Sylow 2-subgroup and every Cayley graph of valency at least four on any group whose derived subgroup is of square-free order.

中文翻译：

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超可解群凯莱图中的无处零 3 流

Tutte 的 3 流猜想断言每个 4 边连通图都承认无处为零的 3 流。我们证明，对于具有非循环 Sylow 2 子群的任何可超解群上的每个价数至少为 4 的凯莱图，以及在其派生子群具有无平方序的任何群上的价数至少为 4 的凯莱图，这个猜想是成立的。