The Complete Solution of Decompositionof Complete Graph into Three Factorswith Diameter
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چکیده
In this paper we show that the complete graph K 12 is not decomposable into three factors with diameter two, which completes the solution of the problem of decomposition of complete graph into three factors from which the rst one has diameter two and the other factors have nite diameters.
منابع مشابه
Decomposition of complete graphs into factors of diameter two and three
We analyze a minimum number of vertices of a complete graph that can be decomposed into one factor of diameter 2 and k factors of diameter at most 3. We find exact values for k ≤ 4 and the asymptotic value of the ratio of this number and k when k tends to infinity. We also find the asymptotic value of the ratio of the number of vertices of the smallest complete graph that can be decomposed into...
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In the present paper the question is studied from three points of vieAv whether to any natural number k _> 2 there exists a complete graph decomposable into k factors with diameters two . The affirmative answer to this question is given and some estimations for the minimal possible number of vertices of such a complete graph are deduced . As a corollary it follows that given k diameters di, d2 ...
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تاریخ انتشار 2007