Work

A Generalization of an Ear Decomposition and k‐Trees in Highly Connected Star‐Free Graphs

Year: 2026

Type: article

Abstract: ABSTRACT In this paper, we introduce a generalized version of an ear decomposition, called a ‐spider decomposition, for ‐connected star‐free graphs with . This application enables us to improve a previously known sufficient condition for the existence of a ‐tree in highly connected star‐free graphs, where a ‐tree is a spanning tree in which every vertex is of degree at most . More precisely, we show that every ‐connected ‐free graph has a ‐tree for , thereby improving a classical result of Jackson and Wormald for . Our approach differs from previous studies based on toughness‐type arguments and instead relies on both a ‐spider decomposition and a factor theorem related to Hall's marriage theorem.

Source: Journal of Graph Theory

DOI: 10.1002/jgt.70153

Authors: Shun‐ichi Maezawa, Kenta Ozeki, Masaki Yamamoto, Takamasa Yashima

Institutions: Nihon University, Yokohama National University, Seikei University, Kanazawa Institute of Technology

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: Japan Society for the Promotion of Science, Research Institute for Mathematical Sciences

OpenAlex ID: W4415192170

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