# Fast Exact Algorithm for L(2,1)-Labeling of Graphs

Abstract : 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 $O*(2.6488^n)$. 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.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-00607169
Contributor : Mathieu Liedloff <>
Submitted on : Friday, July 8, 2011 - 7:19:43 AM
Last modification on : Thursday, January 17, 2019 - 3:06:04 PM

### Citation

Konstanty Junosza-Szaniawski, Jan Kratochvil, Mathieu Liedloff, Peter Rossmanith, Pawel Rzazewski. Fast Exact Algorithm for L(2,1)-Labeling of Graphs. TAMC 2011 : Theory and Applications of Models of Computation - 8th Annual Conference, May 2011, Tokyo, Japan. pp.82-93, ⟨10.1007/978-3-642-20877-5_9⟩. ⟨hal-00607169⟩

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