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

Abstract

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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.

How to cite

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Zdeněk 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

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 [5] A. Kaneko and K. Ota, The flower property implies 1-toughness and the existence of a 2-factor, Manuscript (unpublished). 

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