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The definition of block is Block of $G$ is a maximal subgraph $G'$ of $G$ with no cut vertex of $G'$ itself. Of course, there can exist many blocks in $G$. In particular, isolated vertices, edges in ...

Let $\Gamma=(V,E)$ be a connected undirected graph with n vertices such that every vertex has degree at least $4$. Now draw arrows on some of the edges, in such a way that the in-degree of every ...

Let $T$ be the universal covering tree of some finite, connected, non-tree graph, and let $n_0(T)$ be the smallest positive integer such that there exists a graph $G$ (loops and multiple edges allowed)...

Problem. Given a tree do we need fewer lines in 3D than in 2D in order to draw it straightline and crossing-free? (Asked 01.10.2016 by Alexander Wolff on page 20 of Volume 1 of the Lviv Scottish Book)...

Let $\sigma(n,m)$ be the number of trees with $n$ vertices $\{ v_1, \dots, v_n \}$ such that the matching number (the size of a maximum matching) is $m$. I have been trying to compute the value of $\...