Abstract
In a graph G, a subset of vertices is a dissociation set if it induces a subgraph with maximum degree at most 1. A maximal dissociation set of G is a dissociation set which is not a proper subset of any other dissociation sets. A maximum dissociation set is a dissociation set of maximum size. We show that every graph of order n has at most 10n5 maximal dissociation sets, and that every triangle-free graph of order n has at most 6n4 maximal dissociation sets. We also characterize the extremal graphs on which these upper bounds are attained.
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