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On Edge-Colored Graphs Covered by Properly Colored Cycles

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Abstract

We characterize edge-colored graphs in which every edge belongs to some properly colored cycle. We obtain our result by applying a characterization of 1-extendable graphs.

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References

  1. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms, Applications. Springer Monographs in Mathematics. Springer, London, 2001

  2. Diestel, R.: Graph Theory, volume 173 of Graduate Texts in Mathematics. Springer, New York, 2nd edition, 2000

  3. Grossman, J.W., Häggkvist, R.: Alternating cycles in edge-partitioned graphs. J. Combin. Theory Ser. B 34(1), 77–81 (1983)

    Google Scholar 

  4. Little, C.H.C., Grant, D.D., Holton, D.A.: On defect-d matchings in graphs. Discrete Math. 13(1), 41–54 (1975)

    Google Scholar 

  5. Lovász, L., Plummer, M.D.: Matching Theory, volume 29 of Annals of Discrete Mathematics. North-Holland Publishing Co., Amsterdam, 1986

  6. Szeider, S.: Finding paths in graphs avoiding forbidden transitions. Discr. Appl. Math. 126(2–3), 239–251 (2003)

    Google Scholar 

  7. Szeider, S.: On theorems equivalent with Kotzig's result on graphs with unique 1-factors. Ars Combinatoria 73, 53–64 (2004)

    Google Scholar 

  8. Yeo, A.: A note on alternating cycles in edge-coloured graphs. J. Combin. Theory Ser. B 69(2), 222–225 (1997)

    Google Scholar 

  9. Yu, Q.L.: Characterizations of various matching extensions in graphs. Australas. J. Combin. 7, 55–64 (1993)

    Google Scholar 

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Received: April, 2003

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Fleischner, H., Szeider, S. On Edge-Colored Graphs Covered by Properly Colored Cycles. Graphs and Combinatorics 21, 301–306 (2005). https://doi.org/10.1007/s00373-005-0613-4

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  • DOI: https://doi.org/10.1007/s00373-005-0613-4

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