Some conclusion on unique \(k\)-list colorable complete multipartite graphs
type: Item
instance of: scholarly article
title: Some conclusion on unique \(k\)-list colorable complete multipartite graphs
zbMATH Open document ID: 1397.05068
DOI: 10.1155/2013/380861
author: Yanning Wang
author: Xuguang Zhang
author: Yanyan Wang
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: If a graph \(G\) admits a \(k\)-list assignment \(L\) such that \(G\) has a unique \(L\)-coloring, then \(G\) is called uniquely \(k\)-list colorable graph, or U\(k\)LC graph for short. In the process of characterizing U\(k\)LC graphs, the complete multipartite graphs \(K_{1*r,s}\) (\(r,s\in N\)) are often researched. But it is usually not easy to construct the unique \(k\)-list assignment of \(K_{1*r,s}\). In this paper, we give some propositions about the property of the graph \(K_{1*r,s}\) when it is U\(k\)LC, which provide a very significant guide for constructing such list assignment. Then a special example of U\(k\)LC graphs \(K_{1*r,s}\) as a application of these propositions is introduced. The conclusion will pave the way to characterize U\(k\)LC complete multipartite graphs.
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 6950641
Wikidata QID: Q59005656
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/380861
OpenAlex ID: W1972024351
DBLP publication ID: journals/jam/WangWZ13a
description: scientific article; zbMATH DE number 6950641