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Spanning k-Trees of n-Connected Graphs

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Abstract

A tree is called a k-tree if the maximum degree is at most k. We prove the following theorem, by which a closure concept for spanning k-trees of n-connected graphs can be defined. Let k ≥ 2 and n ≥ 1 be integers, and let u and v be a pair of nonadjacent vertices of an n-connected graph G such that deg G (u) + deg G (v) ≥ |G| − 1 − (k − 2)n, where |G| denotes the order of G. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree.

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Authors and Affiliations

  1. Department of Computer and Information Sciences, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan

    Mikio Kano & Hiroo Kishimoto

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  1. Mikio Kano
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  2. Hiroo Kishimoto
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Correspondence to Hiroo Kishimoto.

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Research is supported by Grant-in-Aid for Scientific Research of Japan.

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Kano, M., Kishimoto, H. Spanning k-Trees of n-Connected Graphs. Graphs and Combinatorics 27, 413–418 (2011). https://doi.org/10.1007/s00373-011-1021-6

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