Maximal and maximum dissociation sets in general and triangle-free graphs

Jianhua Tu, Yuxin Li and Junfeng Du

Applied Mathematics and Computation, 2022, vol. 426, issue C

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.

Keywords: Maximal dissociation sets; General graphs; Triangle-free graphs; Extremal graphs (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:426:y:2022:i:c:s0096300322001916

DOI: 10.1016/j.amc.2022.127107

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