Extremal graphs of the $k$-th power of paths
Combinatorics
2020-03-31 v1
Abstract
An extremal graph for a given graph is a graph with maximum number of edges on fixed number of vertices without containing a copy of . The -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 . Applying a deep theorem of Simonovits, we characterize the extremal graphs of the -th power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.
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}
}
Comments
9pages