论文标题
部分可观测时空混沌系统的无模型预测
Linear-sized minors with given edge density
论文作者
论文摘要
事实证明，对于每$ \ varepsilon> 0 $，存在$ k> 0 $，因此对于每个整数$ t \ ge2 $，每个具有至少$ kt $的图表都包含一个未成年人，带有$ t $ dertices and Edge密度，至少$ 1- \ varepsilon $。 Indeed, building on recent work of Delcourt and Postle on linear Hadwiger's conjecture, for $\varepsilon\in(0,\frac{1}{256})$ we can take $K=C\log\log(1/\varepsilon)$ where $C>0$ is a universal constant, which extends their recent $O(t\log\log t)$ bound on the chromatic number of无$ k_t $ binor的图形。
It is proved that for every $\varepsilon>0$, there exists $K>0$ such that for every integer $t\ge2$, every graph with chromatic number at least $Kt$ contains a minor with $t$ vertices and edge density at least $1-\varepsilon$. Indeed, building on recent work of Delcourt and Postle on linear Hadwiger's conjecture, for $\varepsilon\in(0,\frac{1}{256})$ we can take $K=C\log\log(1/\varepsilon)$ where $C>0$ is a universal constant, which extends their recent $O(t\log\log t)$ bound on the chromatic number of graphs with no $K_t$ minor.
