ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Discussiones Mathematicae Graph Theory 15(2) (1995)
179-184 DOI: 10.7151/dmgt.1015
Department of Mathematics, University of West Bohemia
Americká 42, 306 14 Plze, Czech Republic
Lehrstuhl C für Mathematik, Rhein.n-Westf. Techn.
Templergraben 55, D-52062 Aachen, Germany
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.