Abstract:
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.
