Compact cylindrical chromatic scheduling
SIAM Journal on Discrete Mathematics
Investigation on interval edge-colorings of graphs
Journal of Combinatorial Theory Series B
Bipartite graphs and their applications
Bipartite graphs and their applications
On the deficiency of bipartite graphs
Proceedings of the third international conference on Graphs and optimization
Consecutive colorings of the edges of general graphs
Discrete Mathematics
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
Consecutive edge-coloring of the generalized θ-graph
Discrete Applied Mathematics
PATAT'06 Proceedings of the 6th international conference on Practice and theory of automated timetabling VI
A generalization of interval edge-colorings of graphs
Discrete Applied Mathematics
Consecutive edge-colorings of generalized θ-graphs
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
On Eulerian extensions and their application to no-wait flowshop scheduling
Journal of Scheduling
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A problem of no-wait scheduling of zero-one time operations without allowing inserted idle times is considered in the case of open, flow and mixed shop. We show that in the case of open shop this problem is equivalent to the problem of consecutive coloring the edges of a bipartite graph G. In the cases of flow shop and mixed shop this problem is equivalent to the problem of consecutive coloring the edges of G with some additional restrictions. Moreover, in all shops under consideration the problem is shown to be strongly NP-hard. Since such colorings are not always possible when the number of processors m 3 for open shop (m 2 for flow shop), we concentrate on special families of scheduling graphs, e.g. paths and cycles, trees, complete bipartite graphs, which can be optimally colored in polynomial time.