Evènement pour le groupe GT Graphes et Applications

Date 2010-06-08  10:00-11:00
TitreA linear time algorithm for L(2,1)-labeling of trees 
RésuméAn $L(2,1)$-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 NP-hard 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.  
LieuSalle 5, Batiment A29 
OrateurHirotaka Ono 
UrlDepartment of Informatics, Kyushu University, Japan 

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