Question 9
A graph has at least three vertices. Given any three vertices $A$, $B$, $C$ of the graph we can find a path from $A$ to $B$ which does not go through $C$. Prove that we can find two disjoint paths from $A$ to $B$.
[A graph is a finite set of vertices such that each pair of distinct vertices has either zero or one edges joining the vertices. A path from $A$ to $B$ is a sequence of vertices $A_1$, $A_2$, ..., $A_n$ such that $A = A_1$, $B = A_n$ and there is an edge between $A_i$ and $A_{i + 1}$ for $i = 1$, $2$, ..., $n-1$. Two paths from $A$ to $B$ are disjoint if the only vertices they have in common are $A$ and $B$.]
[A graph is a finite set of vertices such that each pair of distinct vertices has either zero or one edges joining the vertices. A path from $A$ to $B$ is a sequence of vertices $A_1$, $A_2$, ..., $A_n$ such that $A = A_1$, $B = A_n$ and there is an edge between $A_i$ and $A_{i + 1}$ for $i = 1$, $2$, ..., $n-1$. Two paths from $A$ to $B$ are disjoint if the only vertices they have in common are $A$ and $B$.]