Maximum Cycle Packing in Eulerian Graphs Using Local Traces

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Abstract

For a graph G = (V,E) and a vertex v ∈ V , let T(v) be a local trace at v, i.e. T(v) is an Eulerian subgraph of G such that every walk W(v), with start vertex v can be extended to an Eulerian tour in T(v).

We prove that every maximum edge-disjoint cycle packing Z* of G induces a maximum trace T(v) at v for every v ∈ V . Moreover, if G is Eulerian then sufficient conditions are given that guarantee that the sets of cycles inducing maximum local traces of G also induce a maximum cycle packing of G.

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  • [1] S. Antonakopulos and L. Zhang Approximation algorithms for grooming in optical network design Theoret. Comput. Sci. 412 (2011) 3738-3751. doi:10.1016/j.tcs.2011.03.034

  • [2] F. Bäbler Über eine spezielle Klasse Euler’scher Graphen Comment. Math. Helv. 27 (1953) 81-100. doi:10.1007/BF02564555

  • [3] V. Bafna and P.A. Pevzner Genome rearrangement and sorting by reversals SIAM J. Comput. 25 (1996) 272-289. doi:10.1137/S0097539793250627

  • [4] A. Caprara Sorting permutations by reversals and Eulerian cycle decompositions SIAM J. Discrete Math. 12 (1999) 91-110. doi:10.1137/S089548019731994X

  • [5] A. Caprara A. Panconesi and R. Rizzi Packing cycles in undirected Graphs J. Algorithms 48 (2003) 239-256. doi:10.1016/S0196-6774(03)00052-X

  • [6] G. Fertin A. Labarre I. Rusu ´E. Tannier and S. Vialette Combinatorics of Genome Rearrangement (MIT Press Cambridge Ma. 2009).

  • [7] J. Harant D. Rautenbach P. Recht and F. Regen Packing edge-disjoint cycles in graphs and the cyclomatic number Discrete Math. 310 (2010) 1456-1462. doi:10.1016/j.disc.2009.07.017

  • [8] J. Harant D. Rautenbach P. Recht I. Schiermeyer and E.-M. Sprengel Packing disjoint cycles over vertex cuts Discrete Math. 310 (2010) 1974-1978. doi:10.1016/j.disc.2010.03.009

  • [9] J. Kececioglu and D. Sankoff Exact and approximation algorithms for sorting by reversals with application to genome rearrangement Algorithmica 13 (1997) 180-210. doi:10.1007/BF01188586

  • [10] M. Krivelevich Z. Nutov M.R. Salvatpour J. Yuster and R. Yuster Approximation algorithms and hardness results for cycle packing problems ACM Trans. Algorithm 3(4)) (2007) Article 48.

  • [11] O. Ore A problem regarding the tracing of graphs Elem. Math. 6 (1951) 49-53.

  • [12] P. Recht and E.-M. Sprengel Packing Euler graphs with traces in: Operations Research Proceedings Klatte Lüthi and Schmedders (Ed(s)) (Heidelberg New York Dordrecht London Springer 2011) 53-58.

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Target audience:

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

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