Celebratio Mathematica — Mirzakhani

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E. S. Mahmoodian and M. Mirzakhani: “Decomposition of complete tripartite graphs into 5-cycles,” pp. 235–241 in Combinatorics advances: Papers presented at the 25th annual Iranian mathematics conference (Tehran, 28–31 March 1994). Edited by C. J. Colbourn and E. S. Mahmoodian. Mathematics and its Applications 329. Kluwer Academic Publishers (Dordrecht), 1995. MR 1366852 Zbl 0837.05088 incollection

A result of Sotteau on the necessary and sufficient conditions for decomposing the complete bipartite graphs into even cycles has been shown in many occasions, that it is a very important tool in the theory of graph decomposition into even cycles. In order to have similar tools in the case of odd cycle decomposition, obviously bipartite graphs are not suitable to be considered. Searching for such tools, we have considered decomposition of complete tripartite graphs, \( K_{r,s,t} \), into 5-cycles. There are some necessary conditions that we have shown their sufficiency in the case of \( r = t \), and some other cases. Our conjecture is that these conditions are always sufficient.

Ebadollah Sayed Mahmoodian	Related
Charles Joseph Colbourn	Related