Discrete Mathematics
Incidence and strong edge colorings of graphs
Discrete Mathematics
Investigation on interval edge-colorings of graphs
Journal of Combinatorial Theory Series B
On incidence coloring and star arboricity of graphs
Discrete Mathematics
Consecutive colorings of the edges of general graphs
Discrete Mathematics
The incidence coloring number of Halin graphs and outerplanar graphs
Discrete Mathematics
Traffic grooming in WDM networks
IEEE Communications Magazine
Interval incidence coloring of bipartite graphs
Discrete Applied Mathematics
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In the paper we consider a new problem of wavelength assigment for multicasts in the optical star networks. We are given a star network in which nodes from a set V are connected to the central node with optical fibres. The central node redirects the incoming signal from a single node on a particular wavelength from a given set of wavelengths to some of the other nodes. The aim is to minimize the total number of used wavelengths, which means that the overall cost of the transmission is minimized (i.e. wavelength conversion or optoelectronic conversion is minimized). This problem can be modelled by a p-fiber coloring of some labelled digraph, where colors assigned to arcs of the digraph correspond to the wavelengths. In the paper we assume the set of all wavelengths of the incoming signals to a particular node forms an interval, i.e. a consecutive set of numbers. We analysed the problem of one-multicast transmission (per node). We constructed polynomial time algorithms for some special classes of graphs: complete k-partite graphs, trees and sub-cubic bipartite graphs.