# On Duality between Local Maximum Stable Sets of a Graph and its Line-Graph - Mathematics > Combinatorics

On Duality between Local Maximum Stable Sets of a Graph and its Line-Graph - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

Abstract: G is a Koenig-Egervary graph provided alphaG+ muG=|VG|, where muG isthe size of a maximum matching and alphaG is the cardinality of a maximumstable set. S is a local maximum stable set of G if S is a maximum stable setof the closed neighborhood of S. Nemhauser and Trotter Jr. proved that anylocal maximum stable set is a subset of a maximum stable set of G. In thispaper we demonstrate that if S is a local maximum stable set, the subgraph Hinduced by the closed neighborhood of S is a Koenig-Egervary graph, and M is amaximum matching in H, then M is a local maximum stable set in the line graphof G.

Author: ** Vadim E. Levit, Eugen Mandrescu**

Source: https://arxiv.org/