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The Kőnig graph process
Random Structures and Algorithms ( IF 1 ) Pub Date : 2020-10-09 , DOI: 10.1002/rsa.20969 Nina Kamčev 1 , Michael Krivelevich 2 , Natasha Morrison 3 , Benny Sudakov 4
Random Structures and Algorithms ( IF 1 ) Pub Date : 2020-10-09 , DOI: 10.1002/rsa.20969 Nina Kamčev 1 , Michael Krivelevich 2 , Natasha Morrison 3 , Benny Sudakov 4
Affiliation
Say that a graph G has property 
if the size of its maximum matching is equal to the order of a minimal vertex cover. We study the following process. Set 
and let e1, e2, … eN be a uniformly random ordering of the edges of Kn, with n an even integer. Let G0 be the empty graph on n vertices. For m ≥ 0, Gm + 1 is obtained from Gm by adding the edge em + 1 exactly if Gm ∪ {em + 1} has property 
. We analyze the behavior of this process, focusing mainly on two questions: What can be said about the structure of GN and for which m will Gm contain a perfect matching?
中文翻译：
柯尼希（Kőnig）图过程
假设图G的最大匹配大小等于最小顶点覆盖的顺序，则该图具有属性。我们研究以下过程。设置并让e 1， e 2，… e N为K n的边的均匀随机排序，其中n为偶数整数。令G 0为n个顶点上的空图。为米 ≥0，了Gm + 1被从得到了Gm通过将边缘ë米 + 1确切地，如果跨导 ∪{ Ë米 +1 }具有属性。我们分析一下这个过程的行为，主要集中在两个问题：什么可约的结构可以说GN和其米将跨导包含一个完美匹配？
更新日期：2020-10-30
if the size of its maximum matching is equal to the order of a minimal vertex cover. We study the following process. Set and let e1, e2, … eN be a uniformly random ordering of the edges of Kn, with n an even integer. Let G0 be the empty graph on n vertices. For m ≥ 0, Gm + 1 is obtained from Gm by adding the edge em + 1 exactly if Gm ∪ {em + 1} has property . We analyze the behavior of this process, focusing mainly on two questions: What can be said about the structure of GN and for which m will Gm contain a perfect matching?
中文翻译：
柯尼希（Kőnig）图过程
假设图G
的最大匹配大小等于最小顶点覆盖的顺序，则该图具有属性。我们研究以下过程。设置并让e 1， e 2，… e N为K n的边的均匀随机排序，其中n为偶数整数。令G 0为n个顶点上的空图。为米 ≥0，了Gm + 1被从得到了Gm通过将边缘ë米 + 1确切地，如果跨导 ∪{ Ë米 +1 }具有属性。我们分析一下这个过程的行为，主要集中在两个问题：什么可约的结构可以说GN和其米将跨导包含一个完美匹配？
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