Spanning trees with a bounded number of leaves in a claw-free graph

Mikio Kano, Aung Kyaw, Haruhide Matsuda, Kenta Ozeki, Akira Saito, Tomoki Yamashita

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

Original languageEnglish
Pages (from-to)137-154
Number of pages18
JournalArs Combinatoria
Volume103
Publication statusPublished - 2012 Jan 1

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Keywords

  • Claw-free graphs
  • Degree sum
  • Leaf
  • Spanning tree

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Kano, M., Kyaw, A., Matsuda, H., Ozeki, K., Saito, A., & Yamashita, T. (2012). Spanning trees with a bounded number of leaves in a claw-free graph. Ars Combinatoria, 103, 137-154.