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Discussiones Mathematicae Graph Theory

2005 | 25 | 3 | 273-289
Tytuł artykułu

Potential forbidden triples implying hamiltonicity: for sufficiently large graphs

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In [1], Brousek characterizes all triples of connected graphs, G₁,G₂,G₃, with $G_i = K_{1,3}$ for some i = 1,2, or 3, such that all G₁G₂ G₃-free graphs contain a hamiltonian cycle. In [8], 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 G₁G₂G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In [6], a characterization was 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. In this paper we consider the question of which triples (including $K_{1,s}$, s ≥ 3) of forbidden subgraphs potentially imply all sufficiently large graphs are hamiltonian. For s ≥ 4 we characterize these families.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
273-289
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-12-20
poprawiono
2005-06-14
Twórcy
autor
• University of Memphis, Memphis, TN 38152, USA
autor
• Emory University, Atlanta, GA 30322, USA
autor
• 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] J. Brousek, Z. Ryjácek and I. Schiermeyer, Forbidden subgraphs, stability and hamiltonicity, 18th British Combinatorial Conference (London, 1997), Discrete Math. 197/198 (1999) 143-155, doi: 10.1016/S0012-365X(98)00229-5.
• [4] G. Chartrand and L. Lesniak, Graphs & Digraphs (3rd Edition, Chapman & Hall, 1996).
• [5] 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.
• [6] R.J. Faudree, R.J. Gould and M.S. Jacobson, Forbidden triples implying hamiltonicity: for all graphs, Discuss. Math. Graph Theory 24 (2004) 47-54, doi: 10.7151/dmgt.1212.
• [7] R.J. Faudree, R.J. Gould and M.S. Jacobson, Forbidden triples including $K_{1,3}$ implying hamiltonicity: for sufficiently large graphs, preprint.
• [8] R.J. Faudree, R.J. Gould, M.S. Jacobson and L. Lesniak, Characterizing forbidden clawless triples implying hamiltonian graphs, Discrete Math. 249 (2002) 71-81, doi: 10.1016/S0012-365X(01)00235-7.
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Bibliografia
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