Determining the L(2,1) L ( 2 , 1 ) -span in polynomial space ?
A k k -L(2,1) L ( 2 , 1 ) -labeling of a graph is a mapping from its vertex set into a set of integers {0,,k} { 0 ,  , k } such that adjacent vertices get labels that differ by at least 2 and vertices in distance 2 get different labels. The main result of the paper is an algorithm finding an optimal L(2,1) L ( 2 , 1 ) -labeling of a graph (i.e. an L(2,1) L ( 2 , 1 ) -labeling in which the largest label is the least possible) in time O?(7.4922n) O ? ( 7.492 2 n ) and polynomial space. Then we adapt our method to obtain a faster algorithm for k k -L(2,1) L ( 2 , 1 ) -labeling, where k k is a small positive constant. Moreover, a new interesting extremal graph theoretic problem is defined and solved.
1 ) polynomial space l(2 1) l ( 2 1 ) -labeling l(2 1 ) l(2 1 ) l ( 2 channel assignment problem exact algorithm redblack graph