Geodesic
Minimum Coverings of Crowns with Cycles and Stars
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 81-88.

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Let F, G and H be graphs. A (G, H)-decomposition of F is a partition of the edge set of F into copies of G and copies of H with at least one copy of G and at least one copy of H. For R ⊆ F, a (G, H)-covering of F with padding R is a (G, H)-decomposition of F + E(R). A (G, H)-covering of F with the smallest cardinality is a minimum (G, H)-covering. This paper gives the solution of finding the minimum (Ck, Sk)-covering of the crown Cn,n−1.
Keywords: cycle, star, covering, decomposition, crown 
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Lin, Jenq-Jong; Jou, Min-Jen. Minimum Coverings of Crowns with Cycles and Stars. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 81-88. http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a5/

[1] H.C. Lee, Multidecompositions of complete bipartite graphs into cycles and stars, Ars Combin. 108 (2013) 355–364.

[2] H.C. Lee, Packing and covering the balanced complete bipartite multigraph with cycles and stars, Discrete Math. Theor. Comput. Sci. 16 (2014) 189–202. https://doi.org/10.46298/DMTCS.2091

[3] H.C. Lee and Z.C. Chen, Maximum packings and minimum coverings of multigraphs with paths and stars, Taiwanese J. Math. 19 (2015) 1341–1357. https://doi.org/10.11650/tjm.19.2015.4456

[4] H.C. Lee and J.J. Lin, Decomposition of the complete bipartite graph with a 1-factor removed into cycles and stars, Discrete Math. 313 (2013) 2354–2358. https://doi.org/10.1016/j.disc.2013.06.014

[5] C. Lin, J.J. Lin and T.W. Shyu, Isomorphic star decomposition of multicrowns and the power of cycles, Ars Combin. 53 (1999) 249–256.

[6] J. Ma, L. Pu and H. Shen, Cycle decompositions of Kn,n − I, SIAM J. Discrete Math. 20 (2006) 603–609. https://doi.org/10.1137/050626363

[7] S. Yamamoto, H. Ikeda, S. Shige-eda, K. Ushio and N. Hamada, On claw decomposition of complete graphs and complete bipartie graphs, Hiroshima Math. J. 5 (1975) 33–42. https://doi.org/10.32917/hmj/1206136782