Abstract
We consider the dihamiltonian decomposition problem for 3- regular graphs. A graph G is dihamiltonian decomposable if in the digraph obtained from G by replacing each edge of G as two directed edges, the set of edges are partitioned into 3 edge-disjoint directed hamiltonian cycles. We suggest some conditions for dihamiltonian decomposition of 3-regular graphs: for a 3-regular graph G, it is dihamiltonian decomposable only if it is bipartite, and it is not dihamiltonian decomposable if the number of vertices is a multiple of 4. Applying these conditions to interconnection network topologies, we investigate dihamiltonian decomposition of cubeconnected cycles, chordal rings, etc.
This work was supported by the Korea Science and Engineering Foundation under grant no. 98-0102-07-01-3.
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© 1999 Springer-Verlag Berlin Heidelberg
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Park, JH., Kim, HC. (1999). Dihamiltonian Decomposition of Regular Graphs with Degree Three. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_24
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DOI: https://doi.org/10.1007/3-540-46784-X_24
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