2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77409This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear inequalities satisfied by $fG$ may be both interesting and accessible. Such would provide inequalities both sharp and subtle on the combinatorial structure of $G$. These may be related to Ramsey theory.12 pages, LaTeX 2e, no figuresCombinatorics05C;52B05text