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IEEE Transactions on Computers
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
Mappings for Conflict-Free Access of Paths in Elementary Data Structures
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Graph labeling and radio channel assignment
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Channel assignment schemes for cellular mobile telecommunication systems: A comprehensive survey
IEEE Communications Surveys & Tutorials
Channel Assignment for Wireless Networks Modelled as d-Dimensional Square Grids
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
A characterisation of optimal channel assignments for cellular and square grid wireless networks
Mobile Networks and Applications
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Given an integer 驴 1, a vector (驴1, 驴2, . . . , 驴驴-1) of nonnegative integers, and an undirected graph G = (V, E), an L(驴1, 驴2, . . . , 驴驴-1)-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that |f(u) - f(v)| 驴 驴i, if d(u,v) = i, 1 驴 i 驴 驴 - 1, where d(u, v) is the distance (i.e. the minimum number of edges) between the vertices u and v. An optimal L(驴1, 驴2, . . . , 驴驴-1)-coloring for G is one using the smallest range 驴 of integers over all such colorings. This problem has relevant application in channel assignment for interference avoidance in wireless networks, where channels (i.e. colors) assigned to interfering stations (i.e. vertices) at distance i must be at least 驴i apart, while the same channel can be reused in vertices whose distance is at least 驴. In particular, in this paper, the L(驴1, 1, . . . , 1)-coloring problem is considered on bidimensional grids and rings.