The 1/3-2/3 Conjecture for Ordered Sets whose Cover Graph is a Forest
The 1/3-2/3 Conjecture for Ordered Sets whose Cover Graph is a Forest
复制标题
覆盖图为森林的有序集的 1/3-2/3 猜想
作者：
I. Zaguia
有序集合P =（V，≤）中的平衡对是V的一对元素（x，y），使得P的线性扩张中x在y之前的比例在真实的区间[1/3，2/3]内。我们定义了好对的概念，并声称任何有好对的有序集都将满足猜想，而且每一个不全序的有序集都有一个好对，它的覆盖图是森林。
A balanced pair in an ordered set P = (V, ≤) is a pair (x, y) of elements of V such that the proportion of linear extensions of P that put x before y is in the real interval [1/3, 2/3]. We define the notion of a good pair and claim any ordered set that has a good pair will satisfy the conjecture and furthermore every ordered set which is not totally ordered and has a forest as its cover graph has a good pair.