2-Distance coloring of planar graph-Reference-Cited by-同舟云学术

2-Distance coloring of planar graph

Published:2020-10-10 Issue:02 Volume:13 Page:2150007
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Bu Yue Hua¹²,Cao Jiao Jiao¹

Affiliation:

1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

2. Xingzhi College of Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

Abstract

The [Formula: see text]-2-distance coloring of graph [Formula: see text] is a mapping [Formula: see text] if any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer [Formula: see text] such that [Formula: see text] has a [Formula: see text]-[Formula: see text]-distance coloring, denoted by [Formula: see text]. The purpose of this paper is to prove that every planar graph [Formula: see text] without [Formula: see text]-cycle and intersecting [Formula: see text]-cycle and [Formula: see text] has [Formula: see text].

Funder

National Natural Science Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830921500075

Reference13 articles.

1. Coloring Powers of Planar Graphs

2. Planar graphs of girth at least five are square (Δ + 2)-choosable

3. Graphs with maximum degreeΔ≥17and maximum average degree less than3are list2-distance(Δ+2)-colorable

4. 2-distance (Δ+2)-coloring of planar graphs with girth six and Δ≥18

5. List 2-distance coloring of planar graphs without short cycles

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