4 problems

A 4-regular graph is a graph in which every vertex has degree 4, and a 3-regular subgraph is a subgraph in which every vertex has degree 3. Berge–Sauer conjecture. Every 4-regular…

For a fixed integer $q\ge 3$, let $n_0(q)$ be an integer threshold. Let $G$ be a 2-connected graph of order $n\ge n_0(q)$, and write $\delta(G)$ for its minimum degree. Liu and Nin…

Let $G$ be a graph. An acyclic subgraph of $G$ is a subgraph containing no cycles, and a degree sequence realized by a subgraph is the tuple of vertex degrees of some subgraph of…

Let $\{\mathbb{G}_n\}_{n\in\mathbb{N}}$ be any sequence of growing subgraphs of $\mathbb{Z}^2$, and let $\{X_n\}_{n\in\mathbb{N}}$ be the independently evolving simple random walk…