On Maximal Fractional Independent Sets in Graphs

Abstract

We study convexity with respect to a definition of fractional independence in a graph \(G\) that is quantified over neighbourhoods rather than edges. The graphs that admit a so-called universal maximal fractional independent set are characterized, as are all such sets. A characterization is given of the maximal fractional independent sets which cannot be obtained as a proper convex combination of two other such sets.