Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Constrained Bipartite Edge Coloring with Applications to Wavelength Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Efficient Wavelength Routing on Directed Fiber Trees
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Graphs and Hypergraphs
Bandwidth allocation in WDM tree networks
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Approximate Constrained Bipartite Edge Coloring
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Recent Advances in Wavelength Routing
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
| Hi-index | 0.00 |
It is a classical result from graph theory that the edges of an l-regular bipartite graph can be colored using exactly l colors so that edges that share an endpoint are assigned different colors. In this paper we study two constrained versions of the bipartite edge coloring problem. - Some of the edges adjacent to a pair of opposite vertices of an l- regular bipartite graph are already colored with S colors that appear only on one edge (single colors) and D colors that appear in two edges (double colors). We show that the rest of the edges can be colored using at most max {min{l + D, 31/2}, l + S+D/2} total colors. We also show that this bound is tight by constructing instances in which max{min{l + D, 31/2}, l + S+D/2} colors are indeed necessary. - Some of the edges of an l-regular bipartite graph are already colored with S colors that appear only on one edge. We show that the rest of the edges can be colored using at most max{l + S/2,S} total colors. We also show that this bound is tight by constructing instances in which max{l + S/2,S} total colors are necessary.