Fast exact algorithm for L(2,1)-labeling of graphs

An L(2,1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2,1)-span of...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 505; pp. 42 - 54
Main Authors:	Junosza-Szaniawski, Konstanty, Kratochvíl, Jan, Liedloff, Mathieu, Rossmanith, Peter, Rzążewski, Paweł
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 23.09.2013 Elsevier
Subjects:	[formula omitted]-labeling Computer Science Data Structures and Algorithms Exponential-time algorithm Graphs Exponential-time algorithm Graphs L(2,1)-labeling
ISSN:	0304-3975, 1879-2294
Online Access:	Get full text
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Summary:	An L(2,1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2,1)-span of a graph is the minimum possible span of its L(2,1)-labelings. We show how to compute the L(2,1)-span of a connected graph in time O∗(2.6488n). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3, with 3 itself seemingly having been the Holy Grail for quite a while. As concerns special graph classes, we are able to solve the problem in time O∗(2.5944n) for claw-free graphs, and in time O∗(2n−r(2+nr)r) for graphs having a dominating set of size r.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2012.06.037