Tutte paths and long cycles in circuit graphs
MC Wigal, X Yu - Journal of Combinatorial Theory, Series B, 2023 - Elsevier
Thomassen proved that 4-connected planar graphs are Hamilton connected by showing that
every 2-connected planar graph G contains a Tutte path P between any two given vertices …
every 2-connected planar graph G contains a Tutte path P between any two given vertices …
Dynamics of cycles in polyhedra I: the isolation lemma
J Kessler, JM Schmidt - Journal of Combinatorial Theory, Series B, 2024 - Elsevier
A cycle C of a graph G is isolating if every component of G− V (C) consists of a single vertex.
We show that isolating cycles in polyhedral graphs can be extended to larger ones: every …
We show that isolating cycles in polyhedral graphs can be extended to larger ones: every …
Large cycles in essentially 4-connected graphs
M Wigal, X Yu - arXiv preprint arXiv:2003.09750, 2020 - arxiv.org
Tutte proved that every 4-connected planar graph contains a Hamilton cycle, but there are 3-
connected $ n $-vertex planar graphs whose longest cycles have length $\Theta …
connected $ n $-vertex planar graphs whose longest cycles have length $\Theta …
On the circumference of essentially 4-connected planar graphs
I Fabrici, J Harant, S Mohr, JM Schmidt - arXiv preprint arXiv:1806.09413, 2018 - arxiv.org
A planar graph is essentially $4 $-connected if it is 3-connected and every of its 3-separators
is the neighborhood of a single vertex. Jackson and Wormald proved that every essentially 4 …
is the neighborhood of a single vertex. Jackson and Wormald proved that every essentially 4 …
[PDF][PDF] Rooted structures in graphs: a project on Hadwiger's conjecture, rooted minors, and Tutte cycles
S Mohr - 2020 - db-thueringen.de
“One of the deepest unsolved problems in graph theory is the following conjecture due to
Hadwiger [...].” These words were chosen by Béla Bollobás, Paul Allen Catlin, and Paul …
Hadwiger [...].” These words were chosen by Béla Bollobás, Paul Allen Catlin, and Paul …
[PDF][PDF] of essentially 4-connected planar triangulations
I Fabrici, J Harant, S Mohr, JM Schmidt - kurims.kyoto-u.ac.jp
Circumference of essentially 4-connected planar triangulations Page 1 Journal of Graph
Algorithms and Applications http://jgaa.info/ vol. 25, no. 1, pp. 121–132 (2021) DOI: 10.7155/jgaa.00552 …
Algorithms and Applications http://jgaa.info/ vol. 25, no. 1, pp. 121–132 (2021) DOI: 10.7155/jgaa.00552 …