Geodesic
Two sufficient conditions for component factors in graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 761-766 Cet article a éte moissonné depuis la source Library of Science

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Let G be a graph. For a set ℋ of connected graphs, a spanning subgraph H of a graph G is called an ℋ-factor of G if each component of H is isomorphic to a member of ℋ. An ℋ-factor is also referred as a component factor. If G-e admits an ℋ-factor for any e∈ E(G), then we say that G is an ℋ-factor deleted graph. Let k≥2 be an integer. In this article, we verify that (i) a graph G admits a {K_1,1,K_1,2,…, K_1,k,𝒯(2k+1)}-factor if and only if its binding number bind(G)≥2/2k+1; (ii) a graph G with δ(G)≥2 is a {K_1,1,K_1,2,…,K_1,k,𝒯(2k+1)}-factor deleted graph if its binding number bind(G)≥2/2k-1.
Keywords: graph, minimum degree, binding number, H-factor, H-factor deleted graph 
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Zhou, Sizhong; Bian, Qiuxiang; Sun, Zhiren. Two sufficient conditions for component factors in graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 3, pp. 761-766. http://geodesic.mathdoc.fr/item/DMGT_2023_43_3_a11/

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