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Link to original content: https://doi.org/10.1007/s00373-007-0768-2
On a Spanning Tree with Specified Leaves | Graphs and Combinatorics Skip to main content
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On a Spanning Tree with Specified Leaves

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Abstract

Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V(G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore’s theorem which guarantees the existence of a Hamilton path connecting any two vertices.

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References

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Authors and Affiliations

  1. Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162–8601, Japan

    Yoshimi Egawa

  2. The Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151–8677, Japan

    Haruhide Matsuda

  3. Department of Mathematics, Asahi University, Hozumi, Gifu, 223–8522, Japan

    Tomoki Yamashita

  4. Department of Mathematics, College of Science and Technology, Nihon University, 1-8 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101–8303, Japan

    Kiyoshi Yoshimoto

Authors
  1. Yoshimi Egawa
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  2. Haruhide Matsuda
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  3. Tomoki Yamashita
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  4. Kiyoshi Yoshimoto
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Corresponding author

Correspondence to Haruhide Matsuda.

Additional information

Dedicated to Professor Hikoe Enomoto on his 60th birthday.

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Egawa, Y., Matsuda, H., Yamashita, T. et al. On a Spanning Tree with Specified Leaves. Graphs and Combinatorics 24, 13–18 (2008). https://doi.org/10.1007/s00373-007-0768-2

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  • DOI: https://doi.org/10.1007/s00373-007-0768-2

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