论文标题
大色数的挖掘物中具有一致限制的细分
Subdivisions with congruence constraints in digraphs of large chromatic number
论文作者
论文摘要
We prove that for every digraph $F$ and every assignment of pairs of integers $(r_e,q_e)_{e \in A(F)}$ to its arcs there exists an integer $N$ such that every digraph $D$ with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $ r_e $ modulo $ q_e $，对于（f）$中的每个$ e \。 这将概括为托马森（Thomassen）对无方向图的指示设定类似结果，同时又产生了他结果的新简短证明。
We prove that for every digraph $F$ and every assignment of pairs of integers $(r_e,q_e)_{e \in A(F)}$ to its arcs there exists an integer $N$ such that every digraph $D$ with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $r_e$ modulo $q_e$, for every $e \in A(F)$. This generalizes to the directed setting the analogous result by Thomassen for undirected graphs, and at the same time yields a novel short proof of his result.
