Density Theorems for Intersection Graphs of t-Monotone Curves
Density Theorems for Intersection Graphs of t-Monotone Curves
复制标题
t-单调曲线交图的密度定理
DOI：
10.1137/12088104x
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发表时间：
2012
影响因子：
0.8
通讯作者：
Andrew Suk
中科院分区：
文献类型：
--
作者：
Andrew Suk
如果其内部最多具有T-Monotone曲线曲线，则平面中的γγ是t-Monotone。简单的NT-超声酮曲线具有至少EN2相交对（不相交对）的简单家族，然后存在两个大小的亚家族F1，f2⊂f的每个大小Δn，因此F1中的每条曲线都相互之间的每条曲线（是脱离F2中的每个曲线），F2中的每条曲线，其中δ仅取决于e。
A curve γ in the plane is t-monotone if its interior has at most t−1 vertical tangent points. A family of t-monotone curves F is simple if any two members intersect at most once. It is shown that if F is a simple family of nt-monotone curves with at least en2 intersecting pairs (disjoint pairs), then there exists two subfamilies F1,F2⊂F of size δn each, such that every curve in F1 intersects (is disjoint to) every curve in F2, where δ depends only on e. We apply these results to find pairwise disjoint edges in simple topological graphs.