Exact Results for Generalized Extremal Problems Forbidding an Even Cycle

Ervin Győri; Zhen He; Zequn Lv; Nika Salia; Casey Tompkins; Kitti Varga; Xiutao Zhu

doi:10.1002/jgt.23219

Exact Results for Generalized Extremal Problems Forbidding an Even Cycle

Ervin Győri, Zhen He, Zequn Lv, Nika Salia^*, Casey Tompkins, Kitti Varga, Xiutao Zhu

^*Corresponding author for this work

Department of Mathematics

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

Abstract

We determine the maximum number of copies of (Formula presented.) in a (Formula presented.) -free (Formula presented.) -vertex graph for all integers (Formula presented.) and sufficiently large (Formula presented.). Moreover, for (Formula presented.) and any integer (Formula presented.), we obtain the maximum number of cycles of length (Formula presented.) in an (Formula presented.) -vertex (Formula presented.) -free bipartite graph.

Original language	English
Journal	Journal of Graph Theory
DOIs	https://doi.org/10.1002/jgt.23219
State	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© 2025 Wiley Periodicals LLC.

Keywords

Turán number
bipartite graphs
cycles
extremal number
generalized extremal number

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1002/jgt.23219

Cite this

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title = "Exact Results for Generalized Extremal Problems Forbidding an Even Cycle",

abstract = "We determine the maximum number of copies of (Formula presented.) in a (Formula presented.) -free (Formula presented.) -vertex graph for all integers (Formula presented.) and sufficiently large (Formula presented.). Moreover, for (Formula presented.) and any integer (Formula presented.), we obtain the maximum number of cycles of length (Formula presented.) in an (Formula presented.) -vertex (Formula presented.) -free bipartite graph.",

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author = "Ervin Gy{\H o}ri and Zhen He and Zequn Lv and Nika Salia and Casey Tompkins and Kitti Varga and Xiutao Zhu",

note = "Publisher Copyright: {\textcopyright} 2025 Wiley Periodicals LLC.",

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T1 - Exact Results for Generalized Extremal Problems Forbidding an Even Cycle

AU - Győri, Ervin

AU - He, Zhen

AU - Lv, Zequn

AU - Salia, Nika

AU - Tompkins, Casey

AU - Varga, Kitti

AU - Zhu, Xiutao

PY - 2025

Y1 - 2025

N2 - We determine the maximum number of copies of (Formula presented.) in a (Formula presented.) -free (Formula presented.) -vertex graph for all integers (Formula presented.) and sufficiently large (Formula presented.). Moreover, for (Formula presented.) and any integer (Formula presented.), we obtain the maximum number of cycles of length (Formula presented.) in an (Formula presented.) -vertex (Formula presented.) -free bipartite graph.

AB - We determine the maximum number of copies of (Formula presented.) in a (Formula presented.) -free (Formula presented.) -vertex graph for all integers (Formula presented.) and sufficiently large (Formula presented.). Moreover, for (Formula presented.) and any integer (Formula presented.), we obtain the maximum number of cycles of length (Formula presented.) in an (Formula presented.) -vertex (Formula presented.) -free bipartite graph.

KW - Turán number

KW - bipartite graphs

KW - cycles

KW - extremal number

KW - generalized extremal number

UR - http://www.scopus.com/inward/record.url?scp=85214349021&partnerID=8YFLogxK

U2 - 10.1002/jgt.23219

DO - 10.1002/jgt.23219

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SN - 0364-9024

JO - Journal of Graph Theory

JF - Journal of Graph Theory

ER -

Exact Results for Generalized Extremal Problems Forbidding an Even Cycle

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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