Spanning trees with at most k leaves in 2-connected K1,r-free graphs

Guantao Chen, Yuan Chen, Zhiquan Hu and Shunzhe Zhang

Applied Mathematics and Computation, 2023, vol. 445, issue C

Abstract: A vertex with degree one and a vertex with degree at least three are called a leaf and a branch vertex in a tree, respectively. In this paper, we obtain that every 2-connected K1,r-free graph G contains a spanning tree with at most k leaves if α(G)≤k+⌈k+1r−3⌉−⌊1|r−k−3|+1⌋, where k≥2 and r≥4. The upper bound is best possible. Furthermore, we prove that if a connected K1,4-free graph G satisfies that α(G)≤2k+5, then G contains either a spanning tree with at most k branch vertices or a block B with α(B)≤2. A related conjecture for 2-connected claw-free graphs is also posed.

Keywords: Spanning tree; Leaf; Independence number; K1,r-free (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:445:y:2023:i:c:s0096300323000115

DOI: 10.1016/j.amc.2023.127842

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