# Extremal problems for forbidden pairs that imply hamiltonicity

Discussiones Mathematicae Graph Theory (1999)

- Volume: 19, Issue: 1, page 13-29
- ISSN: 2083-5892

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topRalph Faudree, and András Gyárfás. "Extremal problems for forbidden pairs that imply hamiltonicity." Discussiones Mathematicae Graph Theory 19.1 (1999): 13-29. <http://eudml.org/doc/270578>.

@article{RalphFaudree1999,

abstract = {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.},

author = {Ralph Faudree, András Gyárfás},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hamiltonian; extremal numbers; forbidden subgraph; dense graphs; sparse graphs},

language = {eng},

number = {1},

pages = {13-29},

title = {Extremal problems for forbidden pairs that imply hamiltonicity},

url = {http://eudml.org/doc/270578},

volume = {19},

year = {1999},

}

TY - JOUR

AU - Ralph Faudree

AU - András Gyárfás

TI - Extremal problems for forbidden pairs that imply hamiltonicity

JO - Discussiones Mathematicae Graph Theory

PY - 1999

VL - 19

IS - 1

SP - 13

EP - 29

AB - 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.

LA - eng

KW - hamiltonian; extremal numbers; forbidden subgraph; dense graphs; sparse graphs

UR - http://eudml.org/doc/270578

ER -

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