4 problems

Let $G$ be a cubic Halin graph of order $n$, where a Halin graph is formed from a tree with no vertices of degree two and a cycle joining its leaves in their planar cyclic order. T…

Let $G\in\mathcal{G}_h$, where $\mathcal{G}_h$ is the family of cubic Halin graphs whose characteristic trees are caterpillars with $h+2$ leaves. Let $\chi'_{st}(G)$ denote the sta…

Let $\operatorname{ex}_{\mathcal{H}}(n,C_6)$ denote the maximum number of edges in an $n$-vertex Halin graph containing no cycle of length $6$. The sharp upper-bound conjecture. Fo…

Vignal's conjecture. The oriented chromatic number of every oriented Halin graph is at most $8$.