在发生关系图中生成最小冗余集和最大不可冗余集
Generating minimal redundant and maximal irredundant sets in incidence graphs
AI总结：
本文研究了在特定图类中生成最小冗余集和最大不可冗余集的问题，证明了某些图类上的可处理性及不可处理性。
摘要：
Boros和Makino已证明，除非P=NP，否则不存在输出多项式时间算法来枚举超图的最小冗余集或最大不可冗余集。对于图，这一问题仍未解决，目前仅有一些可处理的情况。本文聚焦于捕捉发生关系的图类，如双图、共双图和分裂图。关于最大不可冗余集问题，我们证明在共双图上的问题与一般图一样难，但在分裂图和强可排序图上是可处理的，后者是双图的推广。至于最小冗余集的枚举问题，我们首先证明在分裂图和共双图上问题是不可处理的，回答了上述开放问题，并且在（C3,C5,C6,C8）自由图上是可处理的，这是一个与强可排序图不相容的图类，同时也推广了双图。
英文摘要：
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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