All Questions

Let $\Gamma$ be a connected graph with $H^1(\Gamma) \cong \mathbb{Z}^d$. Can we give a lower bound (preferably of the form $\gg d$) on the maximal number of edge-disjoint cycles one can find in $\...

In 1933 Karol Borsuk conjectured the following Can every bounded subset $E$ of $\mathbb{R}^d$ be partitioned into $(d+1)$ sets, each of which has a smaller diameter than $E$? Whilst new to this ...

If for any graph $H$ we define $\alpha(H)$ to be the cardinality of any maximum size indepedent set in $H$. Then under what conditions can any graph $G$ be expressed as a union of $\alpha(G)$ complete ...

The cut norm $||A||\_C$ of a real matrix $A = (a_{i,j}) \in \mathcal{R}^{n\times n}$ is the maximum over all $I \subseteq [n], J \subseteq [n]$ of the quantity $\left|\sum_{i \in I, j \in J}a_{i,j}\...

I would like to know if there exists a version of König's theorem for tripartite $3$-graphs. In other words, let $G = (V,T)$ be a tripartite $3$-graph. That is, $V$ is a set of vertices (with $V$ ...