Graphs, flags and partitions

Details Graphs, flags and partitions Graphs, flags and partitions

1998-09-17

arxiv.org/abs/math/9809092v1

Mathematics

Combinatorics

12 pages, LaTeX 2e, no figures

Scientific paper

This 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.

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