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Decomposition of bipartite graphs into closed trails

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Abstract

Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t 1,..., t p ) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T 1,..., t p ) of pairwise edge-disjoint closed trails in G such that T i is of length T i for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M a,a is a perfect matching in K a,a , then the graph K a,a -M a,a is arbitrarily decomposable into closed trails.

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Authors and Affiliations

  1. AGH University of Science and Technology, Al. Mickiewicza 30, 30-059, Kraków, Poland

    Sylwia Cichacz & Mirko Horňák

Authors
  1. Sylwia Cichacz
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  2. Mirko Horňák
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Correspondence to Sylwia Cichacz.

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Cichacz, S., Horňák, M. Decomposition of bipartite graphs into closed trails. Czech Math J 59, 129–144 (2009). https://doi.org/10.1007/s10587-009-0009-3

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  • DOI: https://doi.org/10.1007/s10587-009-0009-3

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