Geodesic
Mycielskians and matchings
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 261-266.

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It is shown in this note that some matching-related properties of graphs, such as their factor-criticality, regularizability and the existence of perfect 2-matchings, are preserved when iterating Mycielski's construction.
Keywords: Mycielskian, factor-critical graph, perfect matching, perfect 2-matching 
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Doslić, Tomislav. Mycielskians and matchings. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 261-266. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a4/

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