4‐Connected 1‐Planar Chordal Graphs Are Hamiltonian‐Connected

Licheng Zhang; Yuanqiu Huang; Shengxiang Lv; Fengming Dong

doi:10.1002/jgt.23250

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4‐Connected 1‐Planar Chordal Graphs Are Hamiltonian‐Connected

Licheng Zhang Yuanqiu Huang Shengxiang Lv Fengming Dong

Year: 2025 Journal: Journal of Graph Theory Vol: 110 (1)Pages: 72-81 Publisher: Wiley

DOI: 10.1002/jgt.23250

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Abstract

ABSTRACT Tutte proved that 4‐connected planar graphs are Hamiltonian. It is unknown if there is an analogous result on 1‐planar graphs. In this paper, we characterize 4‐connected 1‐planar chordal graphs and show that all such graphs are Hamiltonian‐connected. A crucial tool used in our proof is a characteristic of 1‐planar 4‐trees.

Keywords:

Chordal graph Planar graph Mathematics Combinatorics Outerplanar graph Planar Planar straight-line graph Indifference graph Clique-sum Discrete mathematics Hamiltonian (control theory) Polyhedral graph Pathwidth 1-planar graph Graph Computer science Line graph

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Advanced Graph Theory Research

Physical Sciences → Computer Science → Computational Theory and Mathematics

Computational Geometry and Mesh Generation

Physical Sciences → Computer Science → Computer Graphics and Computer-Aided Design

Cellular Automata and Applications

Physical Sciences → Computer Science → Computational Theory and Mathematics

4‐Connected 1‐Planar Chordal Graphs Are Hamiltonian‐Connected

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