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Uniformly Resolvable Cycle Decompositions with Four Different Factors

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Abstract

In this paper, we consider uniformly resolvable decompositions of complete graph \(K_v\)(or \(K_v\) minus a 1-factor I for even v) into cycles. We will focus on the existence of factorizations of \(K_v\) or \(K_v-I\) containing up to four non-isomorphic factors. We obtain all possible solutions for uniform factors involving 4, m, 2m and 4m-cycles with a few possible exceptions when m is odd.

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Authors and Affiliations

  1. Department of Engineering Sciences, Faculty of Engineering, Istanbul University, Avcilar, 34320, Istanbul, Turkey

    Uğur Odabaşı

  2. Department of Mathematics, Gebze Technical University, 41400, Gebze, Kocaeli, Turkey

    Sibel Özkan

Authors
  1. Uğur Odabaşı
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  2. Sibel Özkan
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Correspondence to Uğur Odabaşı.

Additional information

This work is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) under project number 113F033.

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Odabaşı, U., Özkan, S. Uniformly Resolvable Cycle Decompositions with Four Different Factors. Graphs and Combinatorics 33, 1591–1606 (2017). https://doi.org/10.1007/s00373-017-1856-6

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  • DOI: https://doi.org/10.1007/s00373-017-1856-6

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