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.
Similar content being viewed by others
References
Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms, Applications. Springer Monographs in Mathematics. Springer, London, 2001
Diestel, R.: Graph Theory, volume 173 of Graduate Texts in Mathematics. Springer, New York, 2nd edition, 2000
Grossman, J.W., Häggkvist, R.: Alternating cycles in edge-partitioned graphs. J. Combin. Theory Ser. B 34(1), 77–81 (1983)
Little, C.H.C., Grant, D.D., Holton, D.A.: On defect-d matchings in graphs. Discrete Math. 13(1), 41–54 (1975)
Lovász, L., Plummer, M.D.: Matching Theory, volume 29 of Annals of Discrete Mathematics. North-Holland Publishing Co., Amsterdam, 1986
Szeider, S.: Finding paths in graphs avoiding forbidden transitions. Discr. Appl. Math. 126(2–3), 239–251 (2003)
Szeider, S.: On theorems equivalent with Kotzig's result on graphs with unique 1-factors. Ars Combinatoria 73, 53–64 (2004)
Yeo, A.: A note on alternating cycles in edge-coloured graphs. J. Combin. Theory Ser. B 69(2), 222–225 (1997)
Yu, Q.L.: Characterizations of various matching extensions in graphs. Australas. J. Combin. 7, 55–64 (1993)
Author information
Authors and Affiliations
Additional information
Received: April, 2003
Rights and permissions
About this article
Cite this article
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
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00373-005-0613-4