Question 137
A country has a road network with the following properties: along each road we can go in both directions; between two different towns may exist at most one road; there does not exist a road which connects some town with itself; the road network is a connected graph; there are at least $m$ roads out of any town $(m = \text{const} \ge 3)$. The king of this country wants to go round all the towns, but it turned out that it is impossible. What is the minimum number of towns the country can have?