Extremal graphs of the pth power of paths

Long Tu Yuan

doi:10.1016/j.ejc.2022.103548

Extremal graphs of the pth power of paths

Long Tu Yuan

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

An extremal graph for a given graph H is a graph with the maximum number of edges among all H-free graphs with fixed number of vertices. The pth power of a path is a graph obtained from a path by joining all pairs of vertices with distance at most p. Applying a deep theorem of Simonovits, we characterize the extremal graphs for the pth power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.

Original language	English
Article number	103548
Journal	European Journal of Combinatorics
Volume	104
DOIs	https://doi.org/10.1016/j.ejc.2022.103548
State	Published - Aug 2022

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10.1016/j.ejc.2022.103548

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title = "Extremal graphs of the pth power of paths",

abstract = "An extremal graph for a given graph H is a graph with the maximum number of edges among all H-free graphs with fixed number of vertices. The pth power of a path is a graph obtained from a path by joining all pairs of vertices with distance at most p. Applying a deep theorem of Simonovits, we characterize the extremal graphs for the pth power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.",

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AB - An extremal graph for a given graph H is a graph with the maximum number of edges among all H-free graphs with fixed number of vertices. The pth power of a path is a graph obtained from a path by joining all pairs of vertices with distance at most p. Applying a deep theorem of Simonovits, we characterize the extremal graphs for the pth power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.

UR - https://www.scopus.com/pages/publications/85129893982

U2 - 10.1016/j.ejc.2022.103548

DO - 10.1016/j.ejc.2022.103548

M3 - 文章

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SN - 0195-6698

VL - 104

JO - European Journal of Combinatorics

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Extremal graphs of the pth power of paths

Abstract

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