On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs
A (k,t)-list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and |⋃v∈V(G)L(v)|=t. A graph G is (k,t)-choosable if G has a proper coloring f such that f(v)∈L(v) for each (k,t)-list assignment L. In 2011, Charoenpanitseri et al. gave a characterization of (...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/690517 |
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| _version_ | 1832568120791793664 |
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| author | Wongsakorn Charoenpanitseri |
| author_facet | Wongsakorn Charoenpanitseri |
| author_sort | Wongsakorn Charoenpanitseri |
| collection | DOAJ |
| description | A (k,t)-list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and |⋃v∈V(G)L(v)|=t. A graph G is (k,t)-choosable if G has a proper coloring f such that f(v)∈L(v) for each (k,t)-list assignment L. In 2011, Charoenpanitseri et al. gave a characterization of (k,t)-choosability of n-vertex graphs when t≥kn-k2-2k+1 and left open problems when t≤kn-k2-2k. Recently, Ruksasakchai and Nakprasit obtain the results when t=kn-k2-2k. In this paper, we extend the results to case t=kn-k2-2k-1. |
| format | Article |
| id | doaj-art-ff42a9f8403a413da80b241778457f63 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ff42a9f8403a413da80b241778457f632025-02-03T00:59:51ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/690517690517On (k,kn-k2-2k-1)-Choosability of n-Vertex GraphsWongsakorn Charoenpanitseri0Department of Mathematics, Faculty of Information Technology, Rangsit University, Pathum Thani 12000, ThailandA (k,t)-list assignment L of a graph G is a mapping which assigns a set of size k to each vertex v of G and |⋃v∈V(G)L(v)|=t. A graph G is (k,t)-choosable if G has a proper coloring f such that f(v)∈L(v) for each (k,t)-list assignment L. In 2011, Charoenpanitseri et al. gave a characterization of (k,t)-choosability of n-vertex graphs when t≥kn-k2-2k+1 and left open problems when t≤kn-k2-2k. Recently, Ruksasakchai and Nakprasit obtain the results when t=kn-k2-2k. In this paper, we extend the results to case t=kn-k2-2k-1.http://dx.doi.org/10.1155/2015/690517 |
| spellingShingle | Wongsakorn Charoenpanitseri On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs International Journal of Mathematics and Mathematical Sciences |
| title | On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs |
| title_full | On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs |
| title_fullStr | On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs |
| title_full_unstemmed | On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs |
| title_short | On (k,kn-k2-2k-1)-Choosability of n-Vertex Graphs |
| title_sort | on k kn k2 2k 1 choosability of n vertex graphs |
| url | http://dx.doi.org/10.1155/2015/690517 |
| work_keys_str_mv | AT wongsakorncharoenpanitseri onkknk22k1choosabilityofnvertexgraphs |