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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10191010" target="_blank" >RIV/00216208:11320/13:10191010 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.tcs.2012.06.037" target="_blank" >http://dx.doi.org/10.1016/j.tcs.2012.06.037</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2012.06.037" target="_blank" >10.1016/j.tcs.2012.06.037</a>

Result language
angličtina
Original language name
Fast exact algorithm for L(2,1)-labeling of graphs
Original language description
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 isthe 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*(2.6488(n)). 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*(2.5944(n))for claw-free graphs, and in time O*(2(n-r)(2 + n/r)(r)) for graphs having a dominating set of size r.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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