Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs
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 UkLC graph for short. In the process of characterizing UkLC graphs, the complete multipartite graphs K1*r,s(r,s∈N) are often researched. But it is usually not easy to...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/380861 |
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| _version_ | 1832567192257822720 |
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| author | Yanning Wang Yanyan Wang Xuguang Zhang |
| author_facet | Yanning Wang Yanyan Wang Xuguang Zhang |
| author_sort | Yanning Wang |
| collection | DOAJ |
| description | 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 UkLC graph for short. In the process of characterizing UkLC graphs, the complete multipartite graphs K1*r,s(r,s∈N) are often researched. But it is usually not easy to construct the unique k-list assignment of K1*r,s. In this paper, we give some propositions about the property of the graph K1*r,s when it is UkLC, which provide a very significant guide for constructing such list assignment. Then a special example of UkLC graphs K1*r,s as a application of these propositions is introduced. The conclusion will pave the way to characterize UkLC complete multipartite graphs. |
| format | Article |
| id | doaj-art-beb4b24ff36640af82b78a8e56741e66 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-beb4b24ff36640af82b78a8e56741e662025-02-03T01:02:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/380861380861Some Conclusion on Unique k-List Colorable Complete Multipartite GraphsYanning Wang0Yanyan Wang1Xuguang Zhang2School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, ChinaSchool of Economics and Management, Yanshan University, Qinhuangdao, Hebei 066004, ChinaKey Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, ChinaIf 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 UkLC graph for short. In the process of characterizing UkLC graphs, the complete multipartite graphs K1*r,s(r,s∈N) are often researched. But it is usually not easy to construct the unique k-list assignment of K1*r,s. In this paper, we give some propositions about the property of the graph K1*r,s when it is UkLC, which provide a very significant guide for constructing such list assignment. Then a special example of UkLC graphs K1*r,s as a application of these propositions is introduced. The conclusion will pave the way to characterize UkLC complete multipartite graphs.http://dx.doi.org/10.1155/2013/380861 |
| spellingShingle | Yanning Wang Yanyan Wang Xuguang Zhang Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs Journal of Applied Mathematics |
| title | Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs |
| title_full | Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs |
| title_fullStr | Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs |
| title_full_unstemmed | Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs |
| title_short | Some Conclusion on Unique k-List Colorable Complete Multipartite Graphs |
| title_sort | some conclusion on unique k list colorable complete multipartite graphs |
| url | http://dx.doi.org/10.1155/2013/380861 |
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