The flower conjecture in special classes of graphs
Zdeněk Ryjáček, Ingo Schiermeyer · Discussiones Mathematicae Graph Theory · 1995
We say that a spanning eulerian subgraph F ae G is a flower in a graph G if there is a vertex u 2 V (G) (called the center of F ) such that all vertices of G except u are of 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.