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## Discussiones Mathematicae Graph Theory

1999 | 19 | 1 | 13-29
Tytuł artykułu

### Extremal problems for forbidden pairs that imply hamiltonicity

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let C denote the claw $K_{1,3}$, N the net (a graph obtained from a K₃ by attaching a disjoint edge to each vertex of the K₃), W the wounded (a graph obtained from a K₃ by attaching an edge to one vertex and a disjoint path P₃ to a second vertex), and $Z_i$ the graph consisting of a K₃ with a path of length i attached to one vertex. For k a fixed positive integer and n a sufficiently large integer, the minimal number of edges and the smallest clique in a k-connected graph G of order n that is CY-free (does not contain an induced copy of C or of Y) will be determined for Y a connected subgraph of either P₆, N, W, or Z₃. It should be noted that the pairs of graphs CY are precisely those forbidden pairs that imply that any 2-connected graph of order at least 10 is hamiltonian. These extremal numbers give one measure of the relative strengths of the forbidden subgraph conditions that imply a graph is hamiltonian.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
13-29
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-02-16
poprawiono
1998-12-08
Twórcy
autor
• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152
autor
• Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary
Bibliografia
• [1] P. Bedrossian, Forbidden subgraph and minimum degree conditions for hamiltonicity, Ph.D Thesis, Memphis State University, 1991.
• [2] J.A. Bondy and U.S.R. Murty, Graph Theory With Applications (Macmillan, London and Elsevier, New York, 1976).
• [3] G. Chartrand and L. Lesniak, Graphs and Digraphs (2nd ed., Wadsworth and Brooks/Cole, Belmont, 1986).
• [4] G. Dirac, Some Theorems on Abstract Graphs, Proc. London Math. Soc. 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69.
• [5] P. Erdős, R.J. Faudree, C.C. Rousseau and R.H. Schelp, On Cycle Complete Graph Ramsey Numbers, J. Graph Theory 2 (1978) 53-64, doi: 10.1002/jgt.3190020107.
• [6] R.J. Faudree, Forbidden Subgraphs and Hamiltonian Properties - A Survey, Congressus Numerantium 116 (1996) 33-52.
• [7] R.J. Faudree, E. Flandrin and Z. Ryjácek, Claw-free Graphs - A Survey, Discrete Math. 164 (1997) 87-147, doi: 10.1016/S0012-365X(96)00045-3.
• [8] R.J. Faudree and R.J. Gould, Characterizing Forbidden Pairs for Hamiltonian Properties, Discrete Math. 173 (1977) 45-60, doi: 10.1016/S0012-365X(96)00147-1.
• [9] J.K. Kim, The Ramsey number R(3,t) has order of magnitude t²/logt, Random Structures Algorithms 7 (1995) 173-207, doi: 10.1002/rsa.3240070302.
• [10] O. Ore, Note on Hamiltonian Circuits, Amer. Math. Monthly 67 (1960) 55, doi: 10.2307/2308928.
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Bibliografia
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