A characterization of absolute retracts of n-chromatic graphs (Q1076682)

A subgraph \(H\) is a retract of \(G\) provided that there exists a homomorphism from \(G\) to \(H\) which fixes each vertex of \(H\). \(H\) is an isometric subgraph if the distance between any two vertices is the same in \(H\) as in \(G\). Let \(AR_ n\) denotethe class of all \(n\)-chromatic graphs \(G\) such that whenever \(G\) is an isometricsubgraph of an \(n\)-chromatic graph \(G'\) there exists a retraction of \(G'\) onto \(G\). The authors give a recursive characterization of \(AR_ n\).