List 2-distance coloring of planar graphs without short cycles-Reference-Cited by-同舟云学术

List 2-distance coloring of planar graphs without short cycles

Published:2016-02-26 Issue:01 Volume:08 Page:1650013
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Bu Yuehua¹²,Shang Chunhui¹

Affiliation:

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

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

Abstract

A 2-distance coloring of [Formula: see text] is a function [Formula: see text]: [Formula: see text], such that for every two distinct vertices [Formula: see text], [Formula: see text] in [Formula: see text], [Formula: see text] if [Formula: see text]. The 2-distance chromatic number of [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] has a [Formula: see text]-[Formula: see text]-distance coloring, denoted by [Formula: see text]. Similarly, the list 2-distance chromatic number of [Formula: see text] is denoted by [Formula: see text]. In this paper, we proved that: (1) for every planar graph with [Formula: see text] and [Formula: see text], [Formula: see text]; (2) for every planar graph with [Formula: see text] and [Formula: see text], [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830916500130

Reference11 articles.

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

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

3. List 2-distance (Δ + 2)-coloring of planar graphs with girth 6 and Δ ≥ 24

4. List 2-distance coloring of planar graphs

5. An optimal square coloring of planar graphs

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