ArticleOriginal scientific text
Title
The flower conjecture in special classes of graphs
Authors 1, 2
Affiliations
- Department of Mathematics, University of West Bohemia
- Lehrstuhl C für Mathematik, Rhein.n-Westf. Techn. Hochschule
Abstract
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
Bibliography
- J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976).
- H. Fleischner, The square of every two-connected graph is hamiltonian, J. Combin. Theory (B) 16 (1974) 29-34, doi: 10.1016/0095-8956(74)90091-4.
- H. Fleischner, In the squares of graphs, hamiltonicity and pancyclicity, hamiltonian connectedness and panconnectedness are equivalent concepts, Monatshefte für Math. 82 (1976) 125-149, doi: 10.1007/BF01305995.
- A. Kaneko, Research problem, Discrete Math., (to appear).
- A. Kaneko and K. Ota, The flower property implies 1-toughness and the existence of a 2-factor, Manuscript (unpublished).
Pages:
179-184
Main language of publication
English
Received
1994-11-28
Published
1995
Exact and natural sciences