DeepAI AI Chat

Are highly connected 1-planar graphs Hamiltonian?

11/06/2019

∙

by Therese Biedl, et al.

∙

∙

It is well-known that every planar 4-connected graph has a Hamiltonian cycle. In this paper, we study the question whether every 1-planar 4-connected graph has a Hamiltonian cycle. We show that this is false in general, even for 5-connected graphs, but true if the graph has a 1-planar drawing where every region is a triangle.

page 1

page 2

page 3

page 4

∙ 06/06/2022

On Hamiltonian-Connected and Mycielski graphs

A graph G is Hamiltonian-connected if there exists a Hamiltonian path be...

0 Ashok Kumar Das, et al. ∙

∙ 02/18/2019

Find Subtrees of Specified Weight and Cycles of Specified Length in Linear Time

We introduce a variant of DFS which finds subtrees of specified weight i...

0 On-Hei Solomon Lo, et al. ∙

∙ 05/28/2018

On the intersection graph of the disks with diameters the sides of a convex n-gon

Given a convex n-gon, we can draw n disks (called side disks) where each...

0 Luis H. Herrera, et al. ∙

∙ 08/29/2022

Strictly-Convex Drawings of 3-Connected Planar Graphs

Strictly-convex straight-line drawings of 3-connected planar graphs in s...

0 Michael A. Bekos, et al. ∙

∙ 10/19/2017

A new constraint of the Hamilton cycle algorithm

Grinberg's theorem is a necessary condition for the planar Hamilton grap...

0 Heping Jiang, et al. ∙

∙ 10/06/2017

Decomposing 4-connected planar triangulations into two trees and one path

Refining a classical proof of Whitney, we show that any 4-connected plan...

0 Kolja Knauer, et al. ∙

∙ 12/15/2019

Small Connected Planar Graph with 1-Cop-Move Number 4

This paper describes a 720-vertex connected planar graph G such that cop...

0 Wei Quan Lim, et al. ∙