The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

Authors:
Tiziana Calamoneri
Affiliations:
Email: calamo@di.uniroma1.it
Venue:
The Computer Journal
Year:
2006

Citing 0
Cited 46

λ-coloring matrogenic graphs

Discrete Applied Mathematics
The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

Discrete Applied Mathematics
Note: On the hole index of L(2,1)-labelings of r-regular graphs

Discrete Applied Mathematics
An $\mbox{O}(n^{1.75})$ Algorithm for L(2,1)-Labeling of Trees

SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
A distance-labelling problem for hypercubes

Discrete Applied Mathematics
Distance-two labellings of Hamming graphs

Discrete Applied Mathematics
Labeling bipartite permutation graphs with a condition at distance two

Discrete Applied Mathematics
A general approach to L(h,k)-label interconnection networks

Journal of Computer Science and Technology
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
Labeling the r-path with a condition at distance two

Discrete Applied Mathematics
On island sequences of labelings with a condition at distance two

Discrete Applied Mathematics
L(j,k)-labelling and maximum ordering-degrees for trees

Discrete Applied Mathematics
Distance constrained labelings of trees

TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
On injective colourings of chordal graphs

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The L(h,1,1)-labelling problem for trees

European Journal of Combinatorics
Note: L(2,1)-Labelings on the composition of n graphs

Theoretical Computer Science
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4

Discrete Applied Mathematics
New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs

Theoretical Computer Science
Parameterized complexity of coloring problems: Treewidth versus vertex cover

Theoretical Computer Science
Group path covering and distance two labeling of graphs

Information Processing Letters
The (2,1)-total labeling number of outerplanar graphs is at most Δ + 2

IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
L(2,1)-labeling of unigraphs

TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
The L(2,1)-labeling of unigraphs

Discrete Applied Mathematics
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
L(h,1,1)-Labeling of outerplanar graphs

SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Exact λ-numbers of generalized Petersen graphs of certain higher-orders and on Möbius strips

Discrete Applied Mathematics
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
Distance three labelings of trees

Discrete Applied Mathematics
L(2,1)-labeling of dually chordal graphs and strongly orderable graphs

Information Processing Letters
A tight upper bound on the (2,1)-total labeling number of outerplanar graphs

Journal of Discrete Algorithms
Optimal gossiping in geometric radio networks in the presence of dynamical faults

Networks
Survey: Randomly colouring graphs (a combinatorial view)

Computer Science Review
Graph coloring with cardinality constraints on the neighborhoods

Discrete Optimization
On real number labelings and graph invertibility

Discrete Applied Mathematics
On L(2,1)-coloring split, chordal bipartite, and weakly chordal graphs

Discrete Applied Mathematics
On L(2,1)-labeling of generalized Petersen graphs

Journal of Combinatorial Optimization
Optimal gossiping in directed geometric radio networks in presence of dynamical faults

MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
On the L(h, k)-labeling of co-comparability graphs

ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
On the L(2,1)-labelings of amalgamations of graphs

Discrete Applied Mathematics
Path covering number and L(2,1)-labeling number of graphs

Discrete Applied Mathematics
Decomposing combinatorial auctions and set packing problems

Journal of the ACM (JACM)
Fast exact algorithm for L(2,1)-labeling of graphs

Theoretical Computer Science
How many wireless resources are needed to resolve the hidden terminal problem?

Computer Networks: The International Journal of Computer and Telecommunications Networking
Circular L(j,k)-labeling number of direct product of path and cycle

Journal of Combinatorial Optimization

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Abstract

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.