The flower conjecture in special classes of graphs

• Autorzy: Zdeněk Ryjáček , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hamiltonian graphs; flower conjecture; square; claw-free graphs

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1995
• Tom: 15
• Numer: 2
• Strony: 179-184

Daty

wydano

1995

otrzymano

1994-11-28

Twórcy

autor

Zdeněk Ryjáček

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

autor

Ingo Schiermeyer

• Lehrstuhl C für Mathematik, Rhein.n-Westf. Techn. Hochschule, Templergraben 55, D-52062 Aachen, Germany

Bibliografia

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• [5] A. Kaneko and K. Ota, The flower property implies 1-toughness and the existence of a 2-factor, Manuscript (unpublished).

Identyfikatory

DOI

10.7151/dmgt.1015