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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1015,
author = {Zden\v ek Ryj\'a\v cek and Ingo Schiermeyer},
title = {The flower conjecture in special classes of graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {179-184},
zbl = {0845.05065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1015}
}
Zdeněk Ryjáček; Ingo Schiermeyer. The flower conjecture in special classes of graphs. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 179-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1015/
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