Geodetic Contraction Games on Trees

Abstract

The geodetic contraction game was introduced by Fraenkel and Harary (Int. J. Game Theor. 18:327–338, 1989). They showed that the problem on trees can be solved by using the algorithm for solving the Hackendot game. However, if we use the algorithm for solving the Hackendot game directly, then it will take $O(n^3)$ time for solving the geodetic contraction game on trees, where n is the number of vertices in a tree. They also posed the following open question: Is there a more efficient strategy to solve the geodetic contraction game on trees? In this paper, we show that the geodetic contraction game on trees can be solved in $O(n\log n)$ time.

Y.-L. Wang—This work is supported under grants MOST 104–2221–E-011–023–MY3 and MOST 105–2221–E–011–086–.