论文标题
Leighton的定理：扩展，限制和准定理
Leighton's Theorem: extensions, limitations, and quasitrees
论文作者
论文摘要
Leighton的定理指出，如果有一个覆盖两个有限图的树$ t $ $ g_1 $和$ g_2 $，则有一个有限的图形$ \ hat g $，由$ t $覆盖，并覆盖$ g_1 $和$ g_2 $。我们证明，此结果不会扩展到树木以外的其他图。即使准材料的自动形态群包含均匀的晶格，也不会通过准确延伸到非规范的覆盖层。但这确实扩展到了准列赛的常规覆盖范围。
Leighton's Theorem states that if there is a tree $T$ that covers two finite graphs $G_1$ and $G_2$, then there is a finite graph $\hat G$ that is covered by $T$ and covers both $G_1$ and $G_2$. We prove that this result does not extend to regular covers by graphs other than trees. Nor does it extend to non-regular covers by a quasitree, even if the automorphism group of the quasitree contains a uniform lattice. But it does extend to regular coverings by quasitrees.
