Take an undirected graph $G=(V,E)$. For any subset $M\subseteq V$, we define ${\rm deg}_M(v)=|\{k\in M:(v,k)\in E\}|$, namely, the number of neighbors of $v$ in $M$.

Is it true that, there exists a subset $M\subseteq V$ such that, for every $v\in M$, ${\rm deg}_M(v)\leq 3$, and for every $v'\in V\setminus M$, ${\rm deg}_M(v')\geq 4$?

Note that, some obvious cases. If nobody are friends, we can simply take $V$ to be the entire set. Similarly, if $G$ is fully connected, then any $4-$element subset work. I tried to reason in the following way, take a maximal (in the sense of cardinality) $M$, such that, for every $v\in M$, ${\rm deg}_M(v)\leq 3$. Now, for any point outside, if it has $\geq 4$ neighbors, we are done. If not, then there are points in $M$, which are neighbors of $v$, such that, their in$-M$ degree is precisely $3$, but this did not lead me to anywhere.