Ramsey proved that for every positive integer $n$, sufficiently large graph contains an induced $K_n$ or $\overline{K}_n$. Among the many extensions of Ramsey's Theorem there is analogue connected graphs: $K_n$, $K_{1,n}$, $P_n$. In this paper, we establish 2-connected graphs. particular, prove exceeding two, one following as subgraph: a subdivision $K_{2,n}$, $K_{2,n}$ with edge between two ve...

Given $d\in \mathbb{N}$, $g\in \mathbb{N} \cup\{0\}$, and an integral vector $\kappa=(k_1,\dots,k_n)$ such that $k_i>-d$ $k_1+\dots+k_n=d(2g-2)$, let $\Omega^d\mathcal{M}_{g,n}(\kappa)$ denote the moduli space of meromorphic $d$-differentials on Riemann surfaces genus $g$ whose zeros poles have orders prescribed by $\kappa$. We show carries a canonical volume form is parallel with respect to it...

In this article we discuss classic theorems from Convex Geometry in the context of topological drawings and beyond. a simple drawing complete graph $$K_n$$ , any two edges share at most one point: either common vertex or point where they cross. Triangles can be viewed as convex sets. This gives link to geometry. As our main result, present generalization Kirchberger’s theorem that is purely com...

Let $L := U_3(11)$. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. In fact, we prove that $L$, $L:2$ and $L:3$ are OD-characterizable, and $L:S_3$ is $5$-fold OD-characterizable.