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Packing Trees Into n-Chromatic Graphs

100%

Gyárfás A.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 1

199-201

We show that if a sequence of trees T1, T2, ..., Tn−1 can be packed into Kn then they can be also packed into any n-chromatic graph.

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Extremal problems for forbidden pairs that imply hamiltonicity

63%

Faudree R., Gyárfás A.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 1

13-29

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.

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2 Discussiones Mathematicae Graph Theory

2 Gyárfás A.

1 Faudree R.

1 2014

1 1999

Wyniki wyszukiwania

Packing Trees Into n-Chromatic Graphs

Extremal problems for forbidden pairs that imply hamiltonicity