- Tytuł:
- On characterization of uniquely 3-list colorable complete multipartite graphs
- Autorzy:
-
Zhao, Yancai
Shan, Erfang - Powiązania:
- https://bibliotekanauki.pl/articles/744543.pdf
- Data publikacji:
- 2010
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
list coloring
complete multipartite graph
uniquely 3-list colorable graph - Opis:
- For each vertex v of a graph G, if there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: $K_{2,2,r}$ r ∈ {4,5,6,7,8}, $K_{2,3,4}$, $K_{1*4,4}$, $K_{1*4,5}$, $K_{1*5,4}$. Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for $K_{2,2,r}$ r ∈ {4,5,6,7,8}, the others have been proved not to be U3LC graphs. In this paper we first prove that $K_{2,2,8}$ is not U3LC graph, and thus as a direct corollary, $K_{2,2,r}$ (r = 4,5,6,7,8) are not U3LC graphs, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2010, 30, 1; 105-114
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł