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I was thinking, that has a name, that has a name, and mathoverflow knew it, it was on the related column on the right. The invariant is often called the bandwidth of a graph. As Professor Rivin alread …

Andrew Suk gives new bounds for general d and a pretty good bound for d=3 http://arxiv.org/abs/1305.5934

All the point sets in this post are in general position. A set of points in $R^d$ is in general position if every $k+1$ points are affinely independent for $k \le d$. If the set contains at least $d+1 …

Mnev's universality theorem claims that any semialgebraic set is the realization space of some oriented matroid. Moreover, the rank of the or matroid can be prescribed in advance. 1.-Are there intere …

Lately there has been a lot of interest on applications of the ham sandwich theorem and related results. There is a bunch of lecture notes and surveys that touch upon the subject. I dont know of any t …

In a 1986 paper, Harer and Zagier proved the recursion: $$(n+1)e(g,n)=(4n-2)e(g,n-1)+(2n-1)(n-1)(2n-3)e(g-1,n-2)$$ where e(g,n) is the number of ways of grouping sides $S_1...S_{2n}$ of a 2n-gon int …