Locally 2-Arc Transitive Graphs, Homogeneous Factorizations, and Partial Linear Spaces

We establish natural bijections between three different classes of combinatorial objects; namely certain families of locally 2-arc transitive graphs, partial linear spaces, and homogeneous factorizations of arc-transitive graphs. Moreover, the bijections intertwine the actions of the relevant automorphism groups. Thus constructions in any of these areas provide examples for the others. (c) 2005 Wiley Periodicals, Inc.