Question 56
Let $G$ be a graph with $n$ vertices. An edge $e$ of $G$ is a dead end if it is possible to partition (the vertices of) $G$ into two sets $A$ and $B$ such that:
- There are at most $2023$ edges of $G$ with one endpoint in $A$ and one endpoint in $B$.
- The edge $e$ has one of its endpoints in $A$ and the other in $B$.
Show that there are at most $2023(n-1)$ dead ends.
- There are at most $2023$ edges of $G$ with one endpoint in $A$ and one endpoint in $B$.
- The edge $e$ has one of its endpoints in $A$ and the other in $B$.
Show that there are at most $2023(n-1)$ dead ends.