Leighton’s theorem : Extensions, limitations and quasitrees
Leighton’s theorem : Extensions, limitations and
quasitrees
复制标题
莱顿定理：扩展、限制和
DOI：
10.2140/agt.2022.22.881
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Sam Shepherd
中科院分区：
文献类型：
--
作者：
M. Bridson;Sam Shepherd
Leighton定理指出，如果有一棵树$T$覆盖两个有限图$G_1$和$G_2$，则存在一个被$T$覆盖并同时覆盖$G_1$和$G_2$的有限图。我们证明了这一结果不能推广到树以外的图的正则覆盖。即使拟树的自同构群包含一致格，它也不能推广到拟树的非正则覆盖。但它确实延伸到了准星体的常规覆盖物。
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.