Automorphism groups of graphs of bounded Hadwiger number
Martin Grohe and Pascal Schweitzer and Daniel Wiebking
我们确定边界Haswiger数字的有限图形的自拟态组的结构。 我们的证明包括对有限边缘瞬态图的结构分析。 特别是,我们表明,对于连接的,无小,边缘瞬态,无双,有限图,自拟态组的非abelian组成因子具有边界顺序。 我们用这个来表明,有界 Hadwiger 数的有限图的自拟态群是通过使用 abelian 组、对称组和有界顺序的组的重复群扩展获得的。
We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, K_h+1-minor-free, edge-transitive, twin-free, finite graphs the non-abelian composition factors of the automorphism group have bounded order. We use this to show that the automorphism groups of finite graphs of bounded Hadwiger number are obtained by repeated group extensions using abel...