T-colorings of graphs: recent results and open problems
Discrete Mathematics - Special issue: advances in graph labelling
Further Results on T-Coloring and Frequency Assignment Problems
SIAM Journal on Discrete Mathematics
On the Maximum Edge Coloring Problem
Approximation and Online Algorithms
Frequency assignments in IEEE 802.11 WLANs with efficient spectrum sharing
Wireless Communications & Mobile Computing
Two hybrid ant algorithms for the general T-colouring problem
International Journal of Bio-Inspired Computation
UHF Taboos-History and Development
IEEE Transactions on Consumer Electronics
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Suppose G is a graph and T is a set of nonnegative integers. A T-coloring of G is an assignment of a positive integer f(x) to each vertex x of G so that if x and y are joined by an edge of G, then |f (x) --- f (y)| is not in T. Here ,the vertices of G are transmitters, an edge represents interference, f(x) is a television or radio channel assigned to x, and T is a set of disallowed separations for channels assigned to interfering transmitters. The span of a T-coloring of G equals max |f (x) --- f (y)| , where the maximum is taken over all edges {x,y}∈E(G) . The minimum order, and minimum span, where the minimum is taken over all T-colorings of G, are denoted by ( ) T xT (G) , and SpT (G), respectively. We will show several previous results of multigraphs, and we also will present a new algorithm to compute SpT (G) of multigraphs.