A column generation algorithm for finding co-3-plexes in chordal graphs
Abstract
In this study, we tackle the problem of finding a maximum \emph{co-3-plex}, which is a subset of vertices of an input graph, inducing a subgraph of maximum degree 2. We focus on the class of chordal graphs. By observing that the graph induced by a co-3-plex in a chordal graph is a set of isolated triangles and induced paths, we reduce the problem of finding a maximum weight co-3-plex in a graph to that of finding a maximum stable set in an auxiliary graph of exponential size. This reduction allows us to derive an exponential variable-sized linear programming formulation for the maximum weighted co-3-plex problem. We show that the pricing subproblem of this formulation reduces to solving a maximum vertex and edge weight induced path. Such a problem is solvable in polynomial time; therefore, this exhibits a polynomial time column generation algorithm solving the maximum co-3-plex problem on chordal graphs. Moreover, this machinery exhibits a new application for the maximum vertex and edge weighted induced path problems.
Keywords
Cite
@article{arxiv.2604.00721,
title = {A column generation algorithm for finding co-3-plexes in chordal graphs},
author = {Alexandre Dupont-Bouillard},
journal= {arXiv preprint arXiv:2604.00721},
year = {2026}
}