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Published in:
2007 | OriginalPaper | Chapter
Note on Characterization of Uniquely 3-List Colorable Complete Multipartite Graphs
Authors : Yongqiang Zhao, Wenjie He, Yufa Shen, Yanning Wang
Published in: Discrete Geometry, Combinatorics and Graph Theory
Publisher: Springer Berlin Heidelberg
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Let
G
be a graph and suppose that for each vertex
v
of
G
, 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. M. Ghebleh and E. S. Mahmoodian characterized uniquely 3-List colorable complete multipartite graphs except for nine graphs. Recently, except for graph
K
2,3,4
, the other eight graphs were shown not to be uniquely 3-list colorable by W. He and Y. Shen, etc. In this paper, it is proved that
K
2,3,4
is not uniquely 3-list colorable, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely.