Extremal problems for forbidden pairs that imply hamiltonicity

• Autorzy: Ralph Faudree , András Gyárfás
• 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.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1999
• Tom: 19
• Numer: 1
• Strony: 13-29

Daty

wydano

1999

otrzymano

1998-02-16

poprawiono

1998-12-08

Twórcy

autor

Ralph Faudree

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152

autor

András Gyárfás

• Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary

Bibliografia

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• [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.
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Identyfikatory

DOI

10.7151/dmgt.1082