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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.

4 votes
1 answer
235 views

Graphs with adjacency matrix depending on associated-vector distances

Let $G$ be a graph of order $n$ such that for each vertex $v$ there are two associated vectors, $f_v, g_v\in R^n$, where $uv\in E(G)$ if and only if $\|f_u - f_v\|^2 \ge \|g_u-g_v\|^2$. ISGCI didn't …
j.s.'s user avatar
  • 519
6 votes
1 answer
122 views

Have this generalization of Indifference graphs been studied before?

Indifference graphs are those graphs $G=(V,E)$ for which there exists a real-valued function $f$ defined on $V(G)$ such that, if $u$ and $v$ are distinct vertices, $|f(u)−f(v)| \lt 1$ if and only if $ …
j.s.'s user avatar
  • 519
0 votes
1 answer
240 views

a block design question: Does every special 1-design admit a partition which respects enough...

Is it possible to show that every 1-design $D$ with $\lambda=4,k=4$ on $v$ points (for $v$ that is a multiple of $3$) contain some 1-design $Q$ with $\lambda=1,k=3$ on $v$ points such that every block …
j.s.'s user avatar
  • 519