Abstract
An undirected routing problem is a pair (G, R) where G and R are undirected graphs such that V(G) = V(R). A solution to an undirected routing problem (G, R) is a set P of undirected paths of G such that, for each edge {u, v} of R, P contains a path between u and v. We say that a set of paths P is k-colorable if each path of P can be colored by one of the k colors so that the paths of the same color are edge disjoint (each edge of G appears at most once in the paths of each single color). Let Q n denote the n-dimensional hypercube, for arbitrary n ≥ 1. We show that a routing problem (Q n, R) always admits a four-colorable solution when R is a matching, i.e., its maximum degree is one.
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© 1997 Springer-Verlag Berlin Heidelberg
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Gu, QP., Tamaki, H. (1997). Multi-color routing in the undirected hypercube. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_9
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DOI: https://doi.org/10.1007/3-540-63890-3_9
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