Geodesic
Perfect Set of Euler Tours of Kp,p,p
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 783-796

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Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence prove Bermond’s conjecture for G = Kp,p,p.
Keywords: compatible Euler tour, line graph, Hamilton cycle decomposition 
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     author = {Govindan, T. and Muthusamy, A.},
     title = {Perfect {Set} of {Euler} {Tours} of {K\protect\textsubscript{p,p,p}}},
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Govindan, T.; Muthusamy, A. Perfect Set of Euler Tours of Kp,p,p. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 783-796. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a0/