All-to-all Routing on Digraph Networks

Abstract: We discuss an open problem and its converse first posed by Dougherty and Faber in [3], "Network routing on regular directed graphs from spanning factorizations." Does every vertex transitive digraph have a spanning 1=factorization? We show relationships between various properties a regular digraph might have: vertex transitivity, left or right cancellation, tree-like or neighborhood preserving spanning factorizations.