3 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 $G$ be a subcubic outerplanar graph, meaning that $G$ is outerplanar and has maximum degree at most $3$. For each positive integer $t$, let $\tau_t(G)$ denote the smallest numb…

Let $G$) be a cubic graph. The Bickle–Phillips conjecture. … If $G$ does not contain $K_4$, then … If $G$ does not contain $K_4-e$, then … The first assertion is known, while the t…