THE FLOWER CONJECTURE IN SPECIAL CLASSES OF GRAPHS
Department of Mathematics, University of West Bohemia
Lehrstuhl C für Mathematik, Rhein.n-Westf. Techn.
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.
1991 Mathematics Subject Classification: 05C45.
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