On the Turán Numbers of Linear Forests in Bipartite Graphs

Tianying Xie; Longtu Yuan

doi:10.1007/s11401-024-0036-2

On the Turán Numbers of Linear Forests in Bipartite Graphs

Tianying Xie^*
, Longtu Yuan^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Science and Technology of China

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

Abstract

A linear forest is a graph consisting of paths. In this paper, the authors determine the maximum number of edges in an (m, n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n ≥ m when m is sufficiently large.

Original language	English
Pages (from-to)	709-732
Number of pages	24
Journal	Chinese Annals of Mathematics. Series B
Volume	45
Issue number	5
DOIs	https://doi.org/10.1007/s11401-024-0036-2
State	Published - Sep 2024

Keywords

05C05
05C35
Bipartite graph
Linear forest
Turán number

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10.1007/s11401-024-0036-2

Cite this

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title = "On the Tur{\'a}n Numbers of Linear Forests in Bipartite Graphs",

abstract = "A linear forest is a graph consisting of paths. In this paper, the authors determine the maximum number of edges in an (m, n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n ≥ m when m is sufficiently large.",

keywords = "05C05, 05C35, Bipartite graph, Linear forest, Tur{\'a}n number",

author = "Tianying Xie and Longtu Yuan",

note = "Publisher Copyright: {\textcopyright} The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024.",

year = "2024",

month = sep,

doi = "10.1007/s11401-024-0036-2",

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T1 - On the Turán Numbers of Linear Forests in Bipartite Graphs

AU - Xie, Tianying

AU - Yuan, Longtu

N1 - Publisher Copyright: © The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024.

PY - 2024/9

Y1 - 2024/9

N2 - A linear forest is a graph consisting of paths. In this paper, the authors determine the maximum number of edges in an (m, n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n ≥ m when m is sufficiently large.

AB - A linear forest is a graph consisting of paths. In this paper, the authors determine the maximum number of edges in an (m, n)-bipartite graph which does not contain a linear forest consisting of paths on at least four vertices for n ≥ m when m is sufficiently large.

KW - 05C05

KW - 05C35

KW - Bipartite graph

KW - Linear forest

KW - Turán number

UR - https://www.scopus.com/pages/publications/85206876366

U2 - 10.1007/s11401-024-0036-2

DO - 10.1007/s11401-024-0036-2

M3 - 文章

AN - SCOPUS:85206876366

SN - 0252-9599

VL - 45

SP - 709

EP - 732

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 5

ER -

On the Turán Numbers of Linear Forests in Bipartite Graphs

Abstract

Keywords

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