On the Turán Number of Forests (original) (raw)

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• Hong Liu
• Bernard Lidicky
• Cory Palmer

Keywords: Graph Theory, Forest, Edges

Abstract

The Turán number of a graph HHH, mathrmex(n,H)\mathrm{ex}(n,H)mathrmex(n,H), is the maximum number of edges in a graph on nnn vertices which does not have HHH as a subgraph. We determine the Turán number and find the unique extremal graph for forests consisting of paths when nnn is sufficiently large. This generalizes a result of Bushaw and Kettle [Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine the Turán number and extremal graphs for forests consisting of stars of arbitrary order.

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How to Cite

Liu, H., Lidicky, B., & Palmer, C. (2013). On the Turán Number of Forests. The Electronic Journal of Combinatorics, 20(2), #P62. https://doi.org/10.37236/3142