Let $G$ be a connected planar graph with $p$ vertices, where $p \geq 3$. Let $t$ denote the number of vertices in $G$ with degree less than $6$.
Prove that if $G$ has no cycles then $t \geq \frac{4p+2}{5}$.
I tried using the inequality $p \leq 3p - 6$ with Euler's formula: $p - q + 1 = 2$ (where $p$ is the number of vertices in G, $q$ is the number of edges in G, $f$ is the number of faces in G) but couldn't figure it out. Thanks in advance!