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(n4). © 1989, Academic Press Limited. All rights reserved.
Bandelt, H. J., & Pesch, E. (1989). DismantlinG Absolute Retracts of Reflexive Graphs. European Journal of Combinatorics, 10(3), 211–220. https://doi.org/10.1016/S0195-6698(89)80053-8