Stable sets versus independent sets
Let G=(V, E) be a graph and let L(G) be the set of stable sets of G. The matroidal number of G, denoted by m(G), is the smallest integer m such that L(G)=J1∪J2∪⋯∪Jm for some matroids Mi=(V,Ji)(i=1,2,...,m). We characterize the graphs of matroidal number at most m for all m≥1. For m≤3, we show that the graphs of matroidal number at most m can be characterized by excluding finitely many induced subgraphs. We also consider a similar problem which replaces 'union' by 'intersection'. © 1993.
Publication Source (Journal or Book title)
Ding, G. (1993). Stable sets versus independent sets. Discrete Mathematics, 117 (1-3), 73-87. https://doi.org/10.1016/0012-365X(93)90325-N