Abstract

In (Aigner, 1988) Aigner conjectured that: 1. Kn(n≥3)is 3-optimal only forn=5and 8. 2. There are only finitely many 3-optimal graphsKm,nfor fixed m. In this paper, the precise result for the complete bipartite graphs K5,n is given and the conjecture 2 is proved.

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