将可平面图收缩为三角剖分的收缩图
Contracting planar graphs to contractions of triangulations
摘要：
对于每一个图$H$，存在一个多项式时间算法来决定平面输入图$G$是否可以收缩为~ $H$。然而，多项式的次数取决于$H$的大小。本文证明了一类图$\cal C$，使得对于每一个$H \in \cal C$，都存在一个在时间上判定可平面图$G$是否可以收缩为~ $H$的算法$f(|V(H)|) \cdot |V(G)|^{\bigO{1}}$. (The函数$f(\cdot)$不依赖于$G$。）类$\cal C$是平面三角剖分图在收缩作用下的闭包。事实上，我们证明了一个图$H \in \cal C$当且仅当存在一个常数$c_H$使得如果一个图的树宽度至少为$c_H$，它包含$H$作为收缩.我们还提供了一个表征的$\cal C$的最小禁止收缩。
英文摘要：
For every graph $H$, there exists a polynomial-time algorithm deciding if a planar input graph $G$ can be contracted to~$H$. However, the degree of the polynomial depends on the size of $H$. In this paper, we identify a class of graphs $\cal C$ such that for every $H \in \cal C$, there exists an algorithm deciding in time $f(|V(H)|) \cdot |V(G)|^{\bigO{1}}$ whether a planar graph $G$ can be contracted to~$H$. (The function $f(\cdot)$ does not depend on $G$.) The class $\cal C$ is the closure of planar triangulated graphs under taking of contractions. In fact, we prove that a graph $H \in \cal C$ if and only if there exists a constant $c_H$ such that if the tree-width of a graph is at least $c_H$, it contains $H$ as a contraction. We also provide a characterization of $\cal C$ in terms of minimal forbidden contractions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
