Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Fixed parameter complexity of λ-labelings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
An exact algorithm for the channel assignment problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4
Discrete Applied Mathematics
Exact Algorithms for L(2,1)-Labeling of Graphs
Algorithmica
On improved exact algorithms for L(2, 1)-labeling of graphs
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
On the computational complexity of the L(2,1)-labeling problem for regular graphs
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Determining the l(2,1)-span in polynomial space
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Determining the L(2,1)-span in polynomial space
Discrete Applied Mathematics
Fast exact algorithm for L(2,1)-labeling of graphs
Theoretical Computer Science
Exact algorithm for graph homomorphism and locally injective graph homomorphism
Information Processing Letters
| Hi-index | 0.89 |
L(2,1)-labeling is a graph coloring model inspired by a frequency assignment in telecommunication. It asks for such a labeling of vertices with nonnegative integers that adjacent vertices get labels that differ by at least 2 and vertices in distance 2 get different labels. It is known that for any k = 4 it is NP-complete to determine if a graph has a L(2,1)-labeling with no label greater than k. In this paper we present a new bound on complexity of an algorithm for finding an optimal L(2,1)-labeling (i.e. an L(2,1)-labeling in which the largest label is the least possible). We improve the upper complexity bound of the algorithm from O^@?(3.5616^n) to O^@?(3.2361^n). Moreover, we establish a lower complexity bound of the presented algorithm, which is @W^@?(3.0739^n).