List injective coloring of a class of planar graphs without short cycles-Reference-Cited by-同舟云学术

List injective coloring of a class of planar graphs without short cycles

Published:2018-10 Issue:05 Volume:10 Page:1850068
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Bu Yuehua¹²,Huang Chaoyuan¹

Affiliation:

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

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

Abstract

An injective [Formula: see text]-coloring of a graph [Formula: see text] is a mapping c: [Formula: see text]([Formula: see text]) [Formula: see text][Formula: see text] such that [Formula: see text] whenever [Formula: see text] have a common neighbor in [Formula: see text]. A list assignment of a graph [Formula: see text] is a mapping [Formula: see text] that assigns a color list [Formula: see text] to each vertex [Formula: see text]. Given a list assignment [Formula: see text] of [Formula: see text], an injective coloring [Formula: see text] of [Formula: see text] is called an injective [Formula: see text]-coloring if [Formula: see text] for every [Formula: see text]. In this paper, we show that if [Formula: see text] is a planar graph with girth [Formula: see text], then [Formula: see text] if [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830918500684

Reference7 articles.

1. Injective coloring of planar graphs

2. LIST INJECTIVE COLORING OF PLANAR GRAPHS WITH GIRTH g ≥ 5

3. Injective Colorings of Graphs with Low Average Degree

4. Some bounds on the injective chromatic number of graphs

5. On the injective chromatic number of graphs

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