The 2-maxian problem on cactus graphs

This paper deals with the 2-maxian problem on cactus graphs. It is shown that in the worst case the midpoint of any path connecting m1 and m2, where {m1,m2} is the 2-maxian of the cactus, lies on a specified cycle. Based on this property, we develop an algorithm with time complexity of O(n2) for the problem on a cactus with n vertices.