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We consider the complexity of the maximum (maximum weight) independent set problem within triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in G−I, there is a vertex w∈I such that {u,v,w} is a triangle in G. We also introduce a new graph parameter (the upper independent neighborhood number) and the corresponding...
An induced matching M of a graph G is a set of pairwise non-adjacent edges such that their end-vertices induce a 1-regular subgraph. An induced matching M is maximal if no other induced matching contains M. The Minimum Maximal Induced Matching problem asks for a minimum maximal induced matching in a given graph. The problem is known to be NP-complete. Here we show that, if P≠NP, for any ε>0, this...
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