4-Connected 1-Planar Chordal Graphs Are Hamiltonian-Connected.
Published in Jounal of Graph Theory, 2025
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. Acrucial tool used in our proof is a characteristic of 1‐planar 4‐trees.