Mathematics > Group Theory
[Submitted on 12 Jan 2014 (v1), last revised 6 Jun 2014 (this version, v2)]
Title:Countable locally 2-arc-transitive bipartite graphs
View PDFAbstract:We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We give several new families of previously unknown countably infinite locally-2-arc-transitive graphs, each family containing continuum many members. These examples are obtained by gluing together copies of incidence graphs of semilinear spaces, satisfying a certain symmetry property, in a tree-like way. In one case we show how the classification problem for that family relates to the problem of determining a certain family of highly arc-transitive digraphs. Numerous illustrative examples are given.
Submission history
From: Robert Gray [view email][v1] Sun, 12 Jan 2014 23:25:36 UTC (42 KB)
[v2] Fri, 6 Jun 2014 09:20:07 UTC (42 KB)
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