Geodesic
Hamilton decompositions of line graphs of some bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 303-310.

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Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).
Keywords: Hamilton cycles, graph decompositions, line graphs 
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Pike, David. Hamilton decompositions of line graphs of some bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 303-310. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a8/

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