Abstract
AbstractWe consider various edge disjoint partitions of complete bipartite graphs. One case is where we decompose the edge set into edge disjoint paths of increasing lengths. A graph G is path‐perfect if there is a positive integer n such that the edge set E(G) of the graph G can be partitioned into paths of length 1,2,3,…,n. The main result of the paper is the proof of the conjecture of Fink and Straight [4]: A complete bipartite graph Ks,t on t + s vertices (t ≤ s) is path‐perfect if and only if there is a positive integer n such that the following two conditions are satisfied; . Our proof gives a linear time algorithm to find an edge disjoint partition of a complete bipartite graph into paths of lengths 1,2,3,…,n. © 2007 Wiley Periodicals, Inc. J Graph Theory 55:91–111, 2007
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