Absolute retracts of bipartite graphs

Abstract A bipartite graph G is an absolute retract if every isometric embedding g of G into a bipartite graph H is a coretraction (that is, there exists an edge-preserving map h from H to G such that hg is the identity map on G ). Examples of absolute retracts are provided by chordal bipartite graphs and the covering graphs of modular lattices of breadth two. We give a construction and several characterizations of bipartite absolute retracts involving Helly type conditions. Bipartite absolute retracts apply to competitive location theory: they are precisely those bipartite graphs on which locational equilibria (Condorcet solutions) always exist. All graphs in this paper are finite, connected, and without loops or multiple edges.