Properly colored C4’s in edge-colored graphs

Chuandong Xu; Colton Magnant; Shenggui Zhang

doi:10.1016/j.disc.2020.112116

Properly colored C₄’s in edge-colored graphs

Chuandong Xu, Colton Magnant, Shenggui Zhang

School of Mathematics and Statistics

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

8 Scopus citations

Abstract

When many colors appear in edge-colored graphs, it is only natural to expect rainbow subgraphs to appear. This anti-Ramsey problem has been studied thoroughly and yet there remain many gaps in the literature. Expanding upon classical and recent results forcing rainbow triangles to appear, we consider similar conditions which force the existence of a properly colored copy of C₄.

Original language	English
Article number	112116
Journal	Discrete Mathematics
Volume	343
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2020.112116
State	Published - Dec 2020

Keywords

Anti-Ramsey number
Color degree
Extremal graph
Properly colored cycle
Threshold graph

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10.1016/j.disc.2020.112116

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title = "Properly colored C4{\textquoteright}s in edge-colored graphs",

abstract = "When many colors appear in edge-colored graphs, it is only natural to expect rainbow subgraphs to appear. This anti-Ramsey problem has been studied thoroughly and yet there remain many gaps in the literature. Expanding upon classical and recent results forcing rainbow triangles to appear, we consider similar conditions which force the existence of a properly colored copy of C4.",

keywords = "Anti-Ramsey number, Color degree, Extremal graph, Properly colored cycle, Threshold graph",

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AU - Xu, Chuandong

AU - Magnant, Colton

AU - Zhang, Shenggui

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AB - When many colors appear in edge-colored graphs, it is only natural to expect rainbow subgraphs to appear. This anti-Ramsey problem has been studied thoroughly and yet there remain many gaps in the literature. Expanding upon classical and recent results forcing rainbow triangles to appear, we consider similar conditions which force the existence of a properly colored copy of C4.

KW - Anti-Ramsey number

KW - Color degree

KW - Extremal graph

KW - Properly colored cycle

KW - Threshold graph

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JO - Discrete Mathematics

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Properly colored C₄’s in edge-colored graphs

Abstract

Keywords

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