A note on spanning trees of connected K_1,t-free graphs whose stems\n have a few leaves

2018/10/18 by Pham Hoang Ha, Ha, Pham Hoang, Dang Dinh Hanh +1
Computer Science · Mathematics · #05C05 #05C07 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1810.08336

openalex publication_date 2018/10/18 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

Abstract

Let T be a tree, a vertex of degree one is called a leaf. The set of leaves\nof T is denoted by Leaf(T). The subtree T-Leaf(T) of T is called the\nstem of T and denoted by Stem(T). In this note, we give a sharp sufficient\ncondition to show that a K_1,t-free graph has a spanning tree whose stem\nhas a few leaves. By applying the main result, we give improvements of previous\nrelated results.\n

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