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arXiv · 2602.18362

Generating minimal redundant and maximal irredundant sets in incidence graphs

Emanuel Castelo·Jérémie Chalopin·Oscar Defrain·Simon Vilmin
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Abstract

It has been proved by Boros and Makino that there is no output-polynomial-time algorithm enumerating the minimal redundant sets or the maximal irredundant sets of a hypergraph, unless P=NP. The same question was left open for graphs, with only a few tractable cases known to date. In this paper, we focus on graph classes that capture incidence relations such as bipartite, co-bipartite, and split graphs. Concerning maximal irredundant sets, we show that the problem on co-bipartite graphs is as hard as in general graphs and tractable in split and strongly orderable graphs, the latter being a generalization of chordal bipartite graphs. As for minimal redundant sets enumeration, we first show that the problem is intractable in split and co-bipartite graphs, answering the aforementioned open question, and that it is tractable on $(C_3,C_5,C_6,C_8)$-free graphs, a class of graphs incomparable to strongly orderable graphs, and which also generalizes chordal bipartite graphs.

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Emanuel Castelo, Jérémie Chalopin, Oscar Defrain, Simon Vilmin. 2026-02-20. Generating minimal redundant and maximal irredundant sets in incidence graphs. https://arxiv.org/abs/2602.18362

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