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- W2078780445 abstract "In this paper, we propose a new closure concept for spanning k-trees. A k-tree is a tree with maximum degree at most k. We prove that: Let G be a connected graph and let u and v be nonadjacent vertices of G. Suppose that $${sum_{w in S}d_G(w) geq |V(G)| -1}$$ for every independent set S in G of order k with $${u,v in S}$$ . Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. This result implies Win’s result (Abh Math Sem Univ Hamburg, 43:263–267, 1975) and Kano and Kishimoto’s result (Graph Comb, 2013) as corollaries." @default.
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- W2078780445 date "2013-04-19" @default.
- W2078780445 modified "2023-10-14" @default.
- W2078780445 title "Closure and Spanning k-Trees" @default.
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- W2078780445 doi "https://doi.org/10.1007/s00373-013-1314-z" @default.
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