A New Greedoid: The Family of Local Maximum Stable Sets of a Forest
| dc.creator | Levit, Vadim E. | |
| dc.creator | Mandrescu, Eugen | |
| dc.date | 1999-12-29 | |
| dc.date.accessioned | 2026-07-07T05:32:32Z | |
| dc.date.available | 2026-07-07T05:32:32Z | |
| dc.description | A maximum stable set in a graph G is a stable set of maximum cardinality. S is a local maximum stable set if it is a maximum stable set of the subgraph of G spanned by the union of S and N(S), where N(S) is the neighborhood of S. One theorem of Nemhauser and Trotter Jr., working as a useful sufficient local optimality condition for the weighted maximum stable set problem, ensures that any local maximum stable set of G can be enlarged to a maximum stable set of G. In this paper we demonstrate that an inverse assertion is true for forests. Namely, we show that for any non-empty local maximum stable set S of a forest T there exists a local maximum stable set S1 of T, such that S1 is included in S and |S1| = |S| - 1. Moreover, as a further strengthening of both the theorem of Nemhauser and Trotter Jr. and its inverse, we prove that the family of all local maximum stable sets of a forest forms a greedoid on its vertex set. | |
| dc.description | A preliminary version of this paper has been presented at DIMACS-RUTCOR Workshop DO'99: Discrete Optimization '99, July 1999, Rutgers University, USA; 10 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/9912222 | |
| dc.identifier | http://arxiv.org/abs/math/9912222 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79688 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C05, 05C69 (Primary) 05B35, 90C10 (Secondary) | |
| dc.title | A New Greedoid: The Family of Local Maximum Stable Sets of a Forest | |
| dc.type | text |