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- W4293490188 abstract "A dissociation set in a graph is a set of vertices inducing a subgraph of maximum degree at most 1. Computing the dissociation number diss(G) of a given graph G, defined as the order of a maximum dissociation set in G, is algorithmically hard even when G is restricted to be bipartite. Recently, Hosseinian and Butenko proposed a simple 43-approximation algorithm for the dissociation number problem in bipartite graphs. Their result relies on the inequality diss(G)≤43α(G−M), where G is a bipartite graph, M is a maximum matching in G, and α(G−M) denotes the independence number of G−M. We show that the pairs (G,M) for which this inequality holds with equality can be recognized efficiently, and that a maximum dissociation set can be determined for them efficiently. The dissociation number of a graph G satisfies max{α(G),2νs(G)}≤diss(G)≤α(G)+νs(G)≤2α(G), where νs(G) denotes the induced matching number of G. We show that deciding whether diss(G) equals any of the four terms α(G), 2νs(G), α(G)+νs(G), and 2α(G) is NP-hard." @default.
- W4293490188 created "2022-08-29" @default.
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- W4293490188 date "2022-12-01" @default.
- W4293490188 modified "2023-10-18" @default.
- W4293490188 title "Relating dissociation, independence, and matchings" @default.
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- W4293490188 doi "https://doi.org/10.1016/j.dam.2022.07.012" @default.
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