Forbidden triples implying Hamiltonicity: for all graphs

• Autorzy: Ralph J. Faudree , Ronald J. Gould , Michael S. Jacobson
• Języki publikacji: EN

Abstrakty

EN

In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with $G_i = K_{1,3}$ for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a $K_{1,s}$, s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being $K_{1,3}$, such that all G₁G₂G₃-free graphs are hamiltonian. This result, together with the triples given by Brousek, completely characterize the forbidden triples G₁, G₂, G₃ such that all G₁G₂G₃-free graphs are hamiltonian.

Słowa kluczowe

EN

hamiltonian; induced subgraph; forbidden subgraphs

Kategorie tematyczne

• 05C35: Extremal problems
• 05C45: Eulerian and Hamiltonian graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 47-54

Daty

wydano

2004

otrzymano

2001-03-15

poprawiono

2003-04-25

Twórcy

autor

Ralph J. Faudree

• University of Memphis, Memphis, TN 38152, USA

autor

Ronald J. Gould

• Emory University, Atlanta, GA 30322, USA

autor

Michael S. Jacobson

• University of Colorado at Denver, Denver, CO 80217, USA

Bibliografia

• [1] P. Bedrossian, Forbidden Subgraph and Minimum Degree Conditions for Hamiltonicity (Ph.D. Thesis, Memphis State University, 1991).
• [2] J. Brousek, Forbidden Triples and Hamiltonicity, Discrete Math. 251 (2002) 71-76, doi: 10.1016/S0012-365X(01)00326-0.
• [3] G. Chartrand and L. Lesniak, Graphs & Digraphs (3rd Edition, Chapman & Hall, 1996).
• [4] R.J. Faudree and R.J. Gould, Characterizing Forbidden Pairs for Hamiltonian Properties, Discrete Math. 173 (1997) 45-60, doi: 10.1016/S0012-365X(96)00147-1.
• [5] R.J. Faudree, R.J. Gould and M.S. Jacobson, Potential Forbidden Triples Implying Hamiltonicity: For Sufficiently Large Graphs, preprint.
• [6] R.J. Faudree, R.J. Gould, M.S. Jacobson and L. Lesniak, Characterizing Forbidden Clawless Triples for Hamiltonian Graphs, Discrete Math. 249 (2002) 71-81, doi: 10.1016/S0012-365X(01)00235-7.

Identyfikatory

DOI

10.7151/dmgt.1212