Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
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)
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
The Channel Assignment Problem with Variable Weights
SIAM Journal on Discrete Mathematics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
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
Exact Exponential Algorithms
On improved exact algorithms for L(2, 1)-labeling of graphs
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
On the complexity of exact algorithm for L (2, 1)-labeling of graphs
Information Processing Letters
Channel assignment via fast zeta transform
Information Processing Letters
Fast exact algorithm for L(2, 1)-labeling of graphs
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Distance constrained labelings of graphs of bounded treewidth
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Locally constrained graph homomorphisms-structure, complexity, and applications
Computer Science Review
Exact algorithms for L(2, 1)-labeling of graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Exact algorithm for graph homomorphism and locally injective graph homomorphism
Information Processing Letters
| Hi-index | 5.23 |
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, with 3 itself seemingly having been the Holy Grail for quite a while. As concerns special graph classes, we are able to solve the problem in time O^*(2.5944^n) for claw-free graphs, and in time O^*(2^n^-^r(2+nr)^r) for graphs having a dominating set of size r.