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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Theoretical Computer Science

ISSN

0304-3975

e-ISSN

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Svazek periodika

505

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

42-54

Kód UT WoS článku

000325905200006

EID výsledku v databázi Scopus

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