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Extremal graphs of the $k$-th power of paths

Combinatorics 2020-03-31 v1

Abstract

An extremal graph for a given graph HH is a graph with maximum number of edges on fixed number of vertices without containing a copy of HH. The kk-th power of a path is a graph obtained from a path and joining all pair of vertices of the path with distance less than kk. Applying a deep theorem of Simonovits, we characterize the extremal graphs of the kk-th power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.

Keywords

Cite

@article{arxiv.2003.12701,
  title  = {Extremal graphs of the $k$-th power of paths},
  author = {Long-Tu Yuan},
  journal= {arXiv preprint arXiv:2003.12701},
  year   = {2020}
}

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9pages