Geodesic
Decomposition of Kn into Dragons
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 275-279

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It is shown that if 1<n ≡ 0 or 1 (mod 2 m), then the edges of Kn may be partitioned into isomorphic copies of a graph D 3(m) and also of a graph D 4(m), graphs consisting respectively of a triangle with an attached path of m - 3 edges or a quadrilateral with an attached path of m - 4 edges. If m is a power of 2 then the above condition is shown to be necessary and sufficient for the existence of such a partition. 
Huang, C.; Schonheim, J. Decomposition of Kn into Dragons. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 275-279. doi: 10.4153/CMB-1980-038-3
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     title = {Decomposition of {Kn} into {Dragons}},
     journal = {Canadian mathematical bulletin},
     pages = {275--279},
     year = {1980},
     volume = {23},
     number = {3},
     doi = {10.4153/CMB-1980-038-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-038-3/}
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