论文标题
在未指向的组标记图中的包装周期
Packing cycles in undirected group-labelled graphs
论文作者
论文摘要
我们证明了罗伯逊（Robertson）和西摩（Seymour）的平壁定理的改进，以$γ$分配给无向图的每个边缘$ g $ g $ g $ g $的每个元素的每个元素$γ$。 As a consequence, we prove that $Γ$-nonzero cycles (cycles whose edges sum to a non-identity element of $Γ$) satisfy the half-integral Erdős-Pósa property, and we also recover a result of Wollan that, if $Γ$ has no element of order two, then $Γ$-nonzero cycles satisfy the Erdős-Pósa property.作为另一个应用程序，我们证明，如果$ m $是一种奇怪的素数，则长度$ \ ell \ mod m $的周期满足所有整数$ \ ell $的Erdős-pósa属性。这部分回答了1987年Dejter和Neumann-Lara的问题，以描述所有这些整数对$（\ ell，m）$。
We prove a refinement of the flat wall theorem of Robertson and Seymour to undirected group-labelled graphs $(G,γ)$ where $γ$ assigns to each edge of an undirected graph $G$ an element of an abelian group $Γ$. As a consequence, we prove that $Γ$-nonzero cycles (cycles whose edges sum to a non-identity element of $Γ$) satisfy the half-integral Erdős-Pósa property, and we also recover a result of Wollan that, if $Γ$ has no element of order two, then $Γ$-nonzero cycles satisfy the Erdős-Pósa property. As another application, we prove that if $m$ is an odd prime power, then cycles of length $\ell \mod m$ satisfy the Erdős-Pósa property for all integers $\ell$. This partially answers a question of Dejter and Neumann-Lara from 1987 on characterizing all such integer pairs $(\ell,m)$.
