Fast exact algorithm for L(2,1)-labeling of graphs
Konstanty Junosza-Szaniawski , Jan Kratochvíl , Mathieu Liedloff , Peter Rossmanith , Paweł Rzążewski
AbstractAn 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 *(2.6488 n ). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3.2361, with 3 seemingly having been the Holy Grail.
|Publication size in sheets||0.6|
|Book||Ogihara Mitsunori, Tarui Jun (eds.): Theory and Applications of Models of Computation, Lecture Notes In Computer Science, vol. 6648, 2011, Springer, ISBN 978-3-642-20876-8|
|Keywords in English||Connected Graph; Exact Algorithm; Input Graph; Common Neighbor; Recursive Call|
|Score|| = 20.0, 22-05-2019, ArticleFromJournal|
= 20.0, 22-05-2019, ArticleFromJournal
|Publication indicators||= 3; = 4|
|Citation count*||7 (2015-04-03)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.