Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Fixed parameter complexity of λ-labelings
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IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
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 complexity of exact algorithm for L (2, 1)-labeling of graphs
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The Computer Journal
Distance constrained labelings of graphs of bounded treewidth
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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Theory of Computing Systems
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A k-L(2,1)-labeling of a graph is a mapping from its vertex set into a set of integers {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)-labeling of a graph (i.e. an L(2,1)-labeling in which the largest label is the least possible) in time O^*(7.4922^n) and polynomial space. Then we adapt our method to obtain a faster algorithm for k-L(2,1)-labeling, where k is a small positive constant. Moreover, a new interesting extremal graph theoretic problem is defined and solved.