# The flower conjecture in special classes of graphs

Zdeněk Ryjáček; Ingo Schiermeyer

Discussiones Mathematicae Graph Theory (1995)

- Volume: 15, Issue: 2, page 179-184
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topZdeněk Ryjáček, and Ingo Schiermeyer. "The flower conjecture in special classes of graphs." Discussiones Mathematicae Graph Theory 15.2 (1995): 179-184. <http://eudml.org/doc/270594>.

@article{ZdeněkRyjáček1995,

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.
},

author = {Zdeněk Ryjáček, Ingo Schiermeyer},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hamiltonian graphs; flower conjecture; square; claw-free graphs; eulerian subgraph; flower; center; flower property; squares},

language = {eng},

number = {2},

pages = {179-184},

title = {The flower conjecture in special classes of graphs},

url = {http://eudml.org/doc/270594},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Zdeněk Ryjáček

AU - Ingo Schiermeyer

TI - The flower conjecture in special classes of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 1995

VL - 15

IS - 2

SP - 179

EP - 184

AB -
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.

LA - eng

KW - hamiltonian graphs; flower conjecture; square; claw-free graphs; eulerian subgraph; flower; center; flower property; squares

UR - http://eudml.org/doc/270594

ER -

## References

top- [1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976). Zbl1226.05083
- [2] 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. Zbl0256.05121
- [3] 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. Zbl0353.05043
- [4] A. Kaneko, Research problem, Discrete Math., (to appear).
- [5] A. Kaneko and K. Ota, The flower property implies 1-toughness and the existence of a 2-factor, Manuscript (unpublished).

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.