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Proper Hamiltonian Paths in Edge-Coloured Multigraphs

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Abstract

Given a c-edge-coloured multigraph, where c is a positive integer, a proper Hamiltonian path is a path that contains all the vertices of the multigraph such that no two adjacent edges have the same colour. In this work we establish sufficient conditions for an edge-coloured multigraph to guarantee the existence of a proper Hamiltonian path, involving various parameters such as the number of edges, the number of colours, the rainbow degree and the connectivity.

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Acknowledgements

The authors would like to thank N. Narayanan for his valuable corrections and comments.

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Authors and Affiliations

  1. Departamento de Análisis Económico y Finanzas, Universidad de Castilla-La Mancha, 45071, Toledo, Spain

    Raquel Águeda

  2. L.R.I., Bât. 650, Université Paris-Sud, 91405, Orsay Cedex, France

    Valentin Borozan, Yannis Manoussakis, Gervais Mendy & Leandro Montero

  3. Departamento de Computación, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina

    Marina Groshaus

Authors
  1. Raquel Águeda
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  2. Valentin Borozan
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  3. Marina Groshaus
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  4. Yannis Manoussakis
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  5. Gervais Mendy
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  6. Leandro Montero
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Correspondence to Leandro Montero.

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Águeda, R., Borozan, V., Groshaus, M. et al. Proper Hamiltonian Paths in Edge-Coloured Multigraphs. Graphs and Combinatorics 33, 617–633 (2017). https://doi.org/10.1007/s00373-017-1803-6

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  • DOI: https://doi.org/10.1007/s00373-017-1803-6

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