4-connected 1-planar chordal graphs are Hamiltonian-connected
Licheng Zhang, Yuanqiu Huang, Shengxiang Lv, Fengming Dong
TL;DR
This paper proves that all 4-connected 1-planar chordal graphs are Hamiltonian-connected, extending Tutte's theorem from planar graphs to a broader class of 1-planar graphs.
Contribution
It characterizes 4-connected 1-planar chordal graphs and demonstrates they are Hamiltonian-connected, a novel extension of classical graph theory results.
Findings
All 4-connected 1-planar chordal graphs are Hamiltonian-connected
Characterization of 4-connected 1-planar chordal graphs
Use of 1-planar 4-trees in the proof
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Interconnection Networks and Systems