
Evènement pour le groupe GT Graphes et Applications
Date  20100608 10:0011:00 
Titre  A linear time algorithm for L(2,1)labeling of trees 
Résumé  An $L(2,1)$labeling of a graph $G$ is an assignment $f$
from the vertex set $V(G)$ to the set of nonnegative integers
such that $f(x)f(y)ge 2$ if $x$ and $y$ are adjacent and
$f(x)f(y)ge 1$ if $x$ and $y$ are at distance 2,
for all $x$ and $y$ in $V(G)$. A $k$$L(2,1)$labeling is
an $L(2,1)$labeling $f:V(G)
ightarrow{0,ldots ,k}$,
and the $L(2,1)$labeling problem asks the minimum $k$,
which we denote by $lambda(G)$, among all possible assignments.
It is known that this problem is NPhard even for graphs of treewidth 2,
and tree is one of very few classes for which the problem is
polynomially solvable. The running time of the best known algorithm
for trees had been $O(Delta^{4.5} n)$ for more than a decade, and
an $mO(min{n^{1.75},Delta^{1.5}n})$time algorithm has appeared recently,
where $Delta$ is the maximum degree of $T$ and $n=V(T)$,
however, it has been open if it is solvable in linear time.
This is a joint work with Toshimasa Ishii, Toru Hasunuma and Yushi Uno.

Lieu  Salle 5, Batiment A29 
Orateur  Hirotaka Ono 
Url  Department of Informatics, Kyushu University, Japan 
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