Set-homogeneous directed graphs

被引：4

作者：

Gray, Robert ^{[1
]}

Macpherson, Dugald ^{[2
]}

Praeger, Cheryl E. ^{[3
]}

Royle, Gordon F. ^{[3
]}

机构：

[1] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

[3] Univ Western Australia, Ctr Math Symmetry & Computat, Sch Math & Stat, Crawley, WA 6009, Australia

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2012年 / 102卷 / 02期

基金：

澳大利亚研究理事会; 英国工程与自然科学研究理事会;

关键词：

Digraphs; Homogeneous structures; Set-homogeneous structures; PERMUTATION-GROUPS; FINITE PRESENTATION; TRANSITIVITY;

D O I：

10.1016/j.jctb.2011.08.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U-g = V. Here, extending work of Lachlan on finite homogeneous digraphs, we classify finite set-homogeneous digraphs, where we allow some pairs of vertices to have arcs in both directions. Under the assumption that such pairs of vertices are not allowed, we obtain initial results on countably infinite set-homogeneous digraphs, classifying those which are not 2-homogeneous. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：474 / 520

页数：47

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