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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

3 votes
0 answers
119 views

Number of spheres in complexes constructed from a Steiner Triple System

Let $M$ be a perfect matching on an even number of vertices $n$, and let $\mathbb{S}_n$ be the symmetric group on $n$ vertices. Next, we construct a graph $G_k := ([n], E)$ using $k$ randomly permuted …
0 votes
0 answers
50 views

Asymptotic bound on the number of simple connected graphs of bounded degree

I have posted this question on Mathematics, but unfortunately no luck so far. Let $\mathcal{G}$ be the family of simple connected graphs on $n$ vertices, where each graph has more than $m$ edges, and …