Geodesic
The flower conjecture in special classes of graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 2, pp. 179-184.

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We say that a spanning eulerian subgraph F ⊂ G is a flower in a graph G if there is a vertex u ∈ V(G) (called the center of F) such that all vertices of G except u are of the degree exactly 2 in F. A graph G has the flower property if every vertex of G is a center of a flower. Kaneko conjectured that G has the flower property if and only if G is hamiltonian. In the present paper we prove this conjecture in several special classes of graphs, among others in squares and in a certain subclass of claw-free graphs.
Keywords: hamiltonian graphs, flower conjecture, square, claw-free graphs 
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Ryjáček, Zdeněk; Schiermeyer, Ingo. The flower conjecture in special classes of graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 2, pp. 179-184. http://geodesic.mathdoc.fr/item/DMGT_1995_15_2_a4/

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