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- W1639885134 abstract "In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise non-adjacent vertices) of the graph. Our analysis shows that the stability number of every graph G can be decomposed in the sum of the stability number of a subgraph containing a perfect 2-matching (i.e. a system of vertex-disjoint odd-cycles and edges covering the vertex-set) plus a term computable in polynomial time. As a consequence, it is possible to bound from above and below the stability number in terms of the matching number of a subgraph having a perfect 2-matching and other quantities computable in polynomial time. Our results are closely related to those by Lorentzen, Balinsky, Spielberg, and Pulleyblank on the linear relaxation of the vertex-cover problem. Moreover, The convex programming problem involved has important applications in information theory and extremal set theory where, as a graph capacity formula, has been used to answer a longstanding open question about qualitatively independet sets in the sense of Renyi (L. Gargano, J. K{o}rner, and U. Vaccaro, Sperner capacities, Graphs and combinatorics, 9:31-46, 1993)." @default.
- W1639885134 created "2016-06-24" @default.
- W1639885134 creator A5002907041 @default.
- W1639885134 date "2003-12-03" @default.
- W1639885134 modified "2023-09-27" @default.
- W1639885134 title "A Splitting Lemma" @default.
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