Abstract
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.
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References
A. Rosa. O cyklických rozkladoch kompletného grafu na nepárnouholniky. Čas. Pěst. Mat, 91: 53–63, 1966.
D. Sotteau. Decomposition of #(m, n) into cycles (circuits) of length 2k. J. of Combinatorial Theory B, 30: 75–81, 1981.
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© 1995 Kluwer Academic Publishers
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Mahmoodian, E.S., Mirzakhani, M. (1995). Decomposition of Complete Tripartite Graphs Into 5-Cycles. In: Colbourn, C.J., Mahmoodian, E.S. (eds) Combinatorics Advances. Mathematics and Its Applications, vol 329. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3554-2_15
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DOI: https://doi.org/10.1007/978-1-4613-3554-2_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3556-6
Online ISBN: 978-1-4613-3554-2
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