Acyclic edge coloring of planar graphs

Acyclic edge coloring of planar graphs

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index of G, denoted by χ′a(G), is the smallest integer k such that G is acyclically edge k-colorable. In this paper, we consider the planar graphs without 3-cycles and...

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Bibliographic Details
Main Authors: Bu, Y. (Author), Jia, Q. (Author), Zhu, H. (Author), Zhu, J. (Author)
Format: Article
Language:English
Published: American Institute of Mathematical Sciences 2022
Subjects:
acyclic edge coloring
cycle
girth
maximum degree
planar graph
Online Access:View Fulltext in Publisher
Description
Summary:An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index of G, denoted by χ′a(G), is the smallest integer k such that G is acyclically edge k-colorable. In this paper, we consider the planar graphs without 3-cycles and intersecting 4-cycles, and prove that χ′a(G) ≤ ∆(G) + 1 if ∆(G) ≥ 8. © 2022 the Author(s), licensee AIMS Press.
ISBN:24736988 (ISSN)
DOI:10.3934/math.2022605

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