EXTREMAL GRAPHS FOR EVEN LINEAR FORESTS IN BIPARTITE GRAPHS

Long Tu Yuan; Xiao Dong Zhang

doi:10.7151/dmgt.2429

EXTREMAL GRAPHS FOR EVEN LINEAR FORESTS IN BIPARTITE GRAPHS

Long Tu Yuan
, Xiao Dong Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Jiao Tong University

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

3 Scopus citations

Abstract

Zarankiewicz proposed the problem of determining the maximum number of edges in an (n, m)-bipartite graph containing no complete bipartite graph K_a,b. In this paper, we consider a variant of the Zarankiewicz problem and determine the maximum number of edges of an (n, m)-bipartite graph without containing a linear forest consisting of even paths. Moveover, all these extremal graphs are characterized in a recursion way.

Original language	English
Pages (from-to)	5-16
Number of pages	12
Journal	Discussiones Mathematicae - Graph Theory
Volume	44
Issue number	1
DOIs	https://doi.org/10.7151/dmgt.2429
State	Published - 2024

Keywords

Turán number
bipartite graph
extremal graph
linear forest

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10.7151/dmgt.2429

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title = "EXTREMAL GRAPHS FOR EVEN LINEAR FORESTS IN BIPARTITE GRAPHS",

abstract = "Zarankiewicz proposed the problem of determining the maximum number of edges in an (n, m)-bipartite graph containing no complete bipartite graph Ka,b. In this paper, we consider a variant of the Zarankiewicz problem and determine the maximum number of edges of an (n, m)-bipartite graph without containing a linear forest consisting of even paths. Moveover, all these extremal graphs are characterized in a recursion way.",

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AU - Yuan, Long Tu

AU - Zhang, Xiao Dong

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AB - Zarankiewicz proposed the problem of determining the maximum number of edges in an (n, m)-bipartite graph containing no complete bipartite graph Ka,b. In this paper, we consider a variant of the Zarankiewicz problem and determine the maximum number of edges of an (n, m)-bipartite graph without containing a linear forest consisting of even paths. Moveover, all these extremal graphs are characterized in a recursion way.

KW - Turán number

KW - bipartite graph

KW - extremal graph

KW - linear forest

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DO - 10.7151/dmgt.2429

M3 - 文章

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SN - 1234-3099

VL - 44

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JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

IS - 1

ER -

EXTREMAL GRAPHS FOR EVEN LINEAR FORESTS IN BIPARTITE GRAPHS

Abstract

Keywords

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