Spanning trees of K1,4-free graphs whose reducible stems have few leaves

Let T be a tree; a vertex of degree 1 is a leaf of T and a vertex of degree at least 3 is a branch vertex of T . The reducible stem of T is the smallest subtree that contains all branch vertices of T . In this paper, we give some sharp sufficient conditions for K 1 , 4 -free graphs to have a spannin...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2024, Vol.89 (1), p.61-71
Main Authors: Ha, Pham Hoang, Nam, Le Dinh, Pham, Ngoc Diep
Format: Article
Language:English
Subjects:
Apexes
Graph theory
Graphs
Mathematics
Mathematics and Statistics
Stems
Trees (mathematics)
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Summary:Let T be a tree; a vertex of degree 1 is a leaf of T and a vertex of degree at least 3 is a branch vertex of T . The reducible stem of T is the smallest subtree that contains all branch vertices of T . In this paper, we give some sharp sufficient conditions for K 1 , 4 -free graphs to have a spanning tree whose reducible stem has few leaves.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-024-00572-7