论文标题
有限的Hadwiger编号图的自多态家组
Automorphism groups of graphs of bounded Hadwiger number
论文作者
论文摘要
我们确定有限的Hadwiger数量有限图的自动形态组的结构。这特别是在1980年代的三个猜想中解决了三个。第一个指出，有限的Hadwiger数字的自动形态群体的非替代，非亚洲组成因子的顺序是有限的。第二个猜想的第二个指出，非平凡的次要封闭图类仅代表有限的许多非亚伯利亚简单组。第三个指出，如果此类组的顺序没有较小的主要因素，那么该组将通过迭代的花圈和从阿贝尔组的直接产品获得。我们的证明包括对有限边缘传输图的结构分析。
We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. This in particular settles three of Babai's conjectures from the 1980s. The first one states that the order of non-alternating, non-abelian composition factors for automorphism groups of graphs of bounded Hadwiger number is bounded. The second one, the subcontraction conjecture, states that a non-trivial minor-closed graph class represents only finitely many non-abelian simple groups. And the third one states that if the order of such a group does not have small prime factors, then the group is obtained by iterated wreath and direct products from abelian groups. Our proof includes a structural analysis of finite edge-transitive graphs.
