ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 19(1) (1999) 13-29
DOI: 10.7151/dmgt.1082


Ralph Faudree

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

András Gyárfás

Computer and Automation Institute
Hungarian Academy of Sciences
Budapest, Hungary


Let C denote the claw K1,3, 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 Zi 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.


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Received 16 February 1998
Revised 8 December 1998