Solution of fink & straight conjecture on path-perfect complete bipartite graphs
نویسندگان
چکیده
We 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; (i) st = 1 + 2 + · · · + n = ( n+1 2 )
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عنوان ژورنال:
- Journal of Graph Theory
دوره 55 شماره
صفحات -
تاریخ انتشار 2007