Forbidding Multiple Copies of Forestable Graphs

Abstract

The Turán number of a graph H is the maximum number of edges in any graph on n vertices which does not contain H as a subgraph. We call a graph Hforestable if it is cyclic, bipartite, and contains a vertex v such that \(H[V\setminus v]\) is a forest. For a forestable graph H, we determine \({\text {ex}}(n,k\cdot H)\) exactly as a function of \({\text {ex}}(n,H)\). This is related to earlier work of the authors on the Turán numbers for equibipartite forests.

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Notes

  1. 1.

    An easy check for the reader—why do we know that the extremal number does not change dramatically when we shift from forbidding a single copy to forbidden several copies of a graph H with chromatic number at least three?

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Correspondence to Neal Bushaw.

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Bushaw, N., Kettle, N. Forbidding Multiple Copies of Forestable Graphs. Graphs and Combinatorics 36, 459–467 (2020). https://doi.org/10.1007/s00373-019-02129-9

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Keywords

  • Turán
  • Extremal
  • Forbidden subgraph
  • Forestable
  • Cycles
  • Bipartite

Mathematics Subject Classification

  • 05C35
  • 05C38