论文标题
一些Mader Perfect Graph类
Some Mader-perfect graph classes
论文作者
论文摘要
$ d $的二分法数，用$ \oferrightarrowχ（d）$表示，是最小的整数$ k $，因此$ d $允许carcyclic $ k $颜色。我们使用$ mader _ {\oferrightArrowχ}（f）$来表示最小的整数$ k $，这样，如果$ \ \toserrightarrowχ（d）\ ge k $，则$ d $包含$ f $的细分。如果每个子$ f $ of $ f $，$ {\ rm mader} _ {\oftrightArrowχ}（f'）= | v（f'）| $，则Digraph $ f $称为Mader Perfect。我们将Octi Digraphs扩展到更大的挖掘物，并证明它是Mader Perfect，它概括了Gishboliner，Steiner和Szabó[Dichromation Number和强制分区，{\ IT J. Comb。理论，Ser。 b} {\ bf 153}（2022）1--30]。我们还表明，如果$ k $是$ \ overLeftrightArrow {c_4} $的适当子数字，除了从$ \ overleftrightArrow {c_4} $获得的digraph通过删除任意弧，那么$ k $是mader-perfect。
The dichromatic number of $D$, denoted by $\overrightarrowχ(D)$, is the smallest integer $k$ such that $D$ admits an acyclic $k$-coloring. We use $mader_{\overrightarrowχ}(F)$ to denote the smallest integer $k$ such that if $\overrightarrowχ(D)\ge k$, then $D$ contains a subdivision of $F$. A digraph $F$ is called Mader-perfect if for every subdigraph $F'$ of $F$, ${\rm mader }_{\overrightarrowχ}(F')=|V(F')|$. We extend octi digraphs to a larger class of digraphs and prove that it is Mader-perfect, which generalizes a result of Gishboliner, Steiner and Szabó [Dichromatic number and forced subdivisions, {\it J. Comb. Theory, Ser. B} {\bf 153} (2022) 1--30]. We also show that if $K$ is a proper subdigraph of $\overleftrightarrow{C_4}$ except for the digraph obtained from $\overleftrightarrow{C_4}$ by deleting an arbitrary arc, then $K$ is Mader-perfect.
