ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 15(2) (1995) 179-184
DOI: 10.7151/dmgt.1015


Zdenk Ryjáček

Department of Mathematics, University of West Bohemia
Americká 42, 306 14 Plze, Czech Republic

Ingo Schiermeyer

Lehrstuhl C für Mathematik, Rhein.n-Westf. Techn. Hochschule
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.


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