On the longest path in a recursively partitionable graph

Julien Bensmail (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A connected graph G with order n is said to be recursively arbitrarily par- titionable (R-AP for short) if either it is isomorphic to K1, or for every se- quence ( tau_1, ..., tau_k) of positive integers summing up to n there exists a partition (V1, ..., Vk) of V (G) such that each Vi induces a connected R-AP subgraph of G on tau_ i vertices. Since previous investigations, it is believed that a R-AP graph should be "almost traceable" somehow. We show that there does not exist a constant c such that every R-AP graph with order n must contain an elementary path on at least n - c vertices for every n.

Mots clés: recursively partitionable graph; longest elementary path

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail. On the longest path in a recursively partitionable graph. 2012. ⟨hal-00718029v1⟩