Geodesic
Degree sum condition for vertex-disjoint 5-cycles
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 555-574

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Let n and k be two integers and G a graph with n=5k vertices. Wang proved that if δ(G)≥ 3k, then G contains k vertex disjoint cycles of length 5. In 2018, Chiba and Yamashita asked whether the degree condition can be replaced by degree sum condition. In this paper, we give a positive answer to this question.
Keywords: degree sum conditions, vertex disjoint 5-cycles 
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Wang, Maoqun; Qian, Jianguo. Degree sum condition for vertex-disjoint 5-cycles. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 555-574. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a7/