DismantlinG Absolute Retracts of Reflexive Graphs

Abstract

Absolute retracts of reflexive graphs are graphs (with loops) for which the systems of all discs have the Helly property. A recursive characterization of these graphs is presented. The main results confirm that the recognition problem is solvable in polynomial time. Two algorithms are available: one is a level test (performed on the distance matrix) and the other is a vertex elimination scheme (operating on the neighbours list). The complexity of either algorithm is O ( n 4 ).