AN ALGORITHM FOR SOLVING MINIMUM EDGE-RANKING SPANNING TREE PROBLEM ON PARTIAL K-TREES
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An edge-ranking of a graph G is a labeling of its edges with positive integers such that every path between two edges with the same label i contains an intermediate edge with label j>i. The minimum edge-ranking spanning tree problem is to find a spanning tree of a graph G whose edge-ranking needs least number of ranks. In this paper, we present an algorithm to solve the minimum edge-ranking spanning tree problem on a partial k-tree G in O(n2∆(k+1)+2 ∆k(k+1)+2 log2k(k+1)+2n) time, where n is the number of vertices, ∆ is the maximum vertex degree of the graph G and k is bounded by a constant value.