The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Algorithms for Square Roots of Graphs
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Journal of Algorithms
On L(d, 1)-labelings of graphs
Discrete Mathematics
A coloring problem on the n-cube
Discrete Applied 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)
New bounds on a hypercube coloring problem
Information Processing Letters
Distance Constrained Labeling of Precolored Trees
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Channel Assignment on Strongly-Simplicial Graphs
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
On a hypercube coloring problem
Journal of Combinatorial Theory Series A
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Computational Complexity of the Distance Constrained Labeling Problem for Trees (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A distance-labelling problem for hypercubes
Discrete Applied Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
An O(n1.75) algorithm for L(2,1)-labeling of trees
Theoretical Computer Science
An exact algorithm for the channel assignment problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
The L(h,1,1)-labelling problem for trees
European Journal of Combinatorics
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
Distance constrained labelings of graphs of bounded treewidth
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
L(2, 1, 1)-labeling is NP-complete for trees
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Elegant distance constrained labelings of trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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An L(2,1,1)-labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that labels of adjacent vertices differ by at least two, while vertices that are at distance at most three are assigned different labels. The maximum label used is called the span of the labeling, and the aim is to minimize this value. We show that the minimum span of an L(2,1,1)-labeling of a tree can be bounded by a lower and an upper bound with difference one. Moreover, we show that deciding whether the minimum span attains the lower bound is an NP-complete problem. This answers a known open problem, which was recently posed by King, Ras, and Zhou as well. We extend some of our results to general graphs and/or to more general distance constraints on the labeling.