The Interval Core of the Minimum Cost Spanning Tree Interval Game and Its Calculation

摘要

In this paper, the minimal cost spanning tree intervalgame is studied. It is proved that the interval core is no emptywhen n=2. By introducing the concepts of the left game, rightgame of MCSTIG, and compositive, it is proved there exists ahyperplane with non-negative normal vector to separate L and Rstrictly. when the interval core of MCSTIG is empty. It obtainedthe sufficient and necessary condition of no empty interval coreof MCSTIG, by using linear programming tools. Finally, thealgorithm to calculate the interval core of MCSTIG is presented.