论文标题
关于几乎稳定的一般旋塞超图的色数
On the chromatic number of almost stable general Kneser hypergraphs
论文作者
论文摘要
令$ n \ ge 1 $和$ s \ ge 1 $为整数。几乎$ s $ stable子集$ a $ a $ of $ [n] = \ {1，\ dots，n \} $是一个子集，以至于对于任何两个不同的元素$ i，j \ in a $ in a $，一个人都有$ | i-j | \ ge s $。对于一个$ [n] $和整数$ r \ ge 2 $的家庭$ \ cal f $，$ r $ r $ r $ - 均匀的kneser kneser kneser hypraph $ \ mbox {kg}^r（{\ cal f}） $ \ cal f $中的成对分离元素的a_r \} $在文献中进行了广泛的研究，Abyazi Sani和Alishahi能够根据可2 $ r $ r $ - 可溶性的缺陷，$ \ mbox {ecd}^r（ecd}^r（{\ cal f}）$。在本文中，修改了所有$ k $ -subsets的特殊家族的陈陈方法，以给定为几乎稳定的稳定的一般性kneser Hypergraph $ \ mbox {kg}^r（{\ cal f} _s）$ $ \ mbox $ \ mbox {ecd} $ car（car（car）的稳定的稳定的通用kneser hyseer hyseer hyseer hyseer hyseer hyseer hyseer hypergraph $ \ mbox {kg}^r（{\ cal f} _s）$的下限。这里$ {\ cal f} _s $是$ \ cal f $的几乎$ s $稳定元素的集合。我们还提出了对Meunier的猜想的概括。
Let $n\ge 1$ and $s\ge 1$ be integers. An almost $s$-stable subset $A$ of $[n]=\{1,\dots,n\}$ is a subset such that for any two distinct elements $i, j\in A$, one has $|i-j|\ge s$. For a family $\cal F$ of non-empty subsets of $[n]$ and an integer $r\ge 2$, the chromatic number of the $r$-uniform Kneser hypergraph $\mbox{KG}^r({\cal F})$, whose vertex set is $\cal F$ and whose edge set is the set of $\{A_1,\dots, A_r\}$ of pairwise disjoint elements in $\cal F$, has been studied extensively in the literature and Abyazi Sani and Alishahi were able to give a lower bound for it in terms of the equatable $r$-colorability defect, $\mbox{ecd}^r({\cal F})$. In this article, the methods of Chen for the special family of all $k$-subsets of $[n]$, are modified to give lower bounds for the chromatic number of almost stable general Kneser hypergraph $\mbox{KG}^r({\cal F}_s)$ in terms of $\mbox{ecd}^s({\cal F})$. Here ${\cal F}_s$ is the collection of almost $s$-stable elements of $\cal F$. We also propose a generalization of a conjecture of Meunier.
