Also available at http://amc-journal.eu ISSN 1855-3966 (printed edn.), ISSN 1855-3974 (electronic edn.) ARS MATHEMATICA CONTEMPORANEA 8 (2015) 177–194 Regular embeddings of cycles with multiple edges revisited Dedicated to Dragan Maruˇ siˇ c on the occasion of his 60th birthday Kan Hu Faculty of Natural Sciences, Matej Bel University, 974 01 Bansk ´ a Bystrica, Slovakia and Institute of Mathematics, Slovak Academy of Sciences, 975 49 Bansk ´ a Bystrica, Slovakia and School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316000, People’s Republic of China Roman Nedela Faculty of Natural Sciences, Matej Bel University, 974 01 Bansk ´ a Bystrica, Slovakia and Institute of Mathematics, Slovak Academy of Sciences, 975 49 Bansk ´ a Bystrica, Slovakia Martin ˇ Skoviera Department of Computer Science, Comenius University, 842 15 Bratislava, Slovakia Naer Wang Faculty of Natural Sciences, Matej Bel University, 974 01 Bansk ´ a Bystrica, Slovakia and School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang 316000, People’s Republic of China Received 10 March 2014, accepted 13 May 2014, published online 28 September 2014 cb This work is licensed under http://creativecommons.org/licenses/by/3.0/