The Kelmans-Seymour conjecture III: 3-vertices in K4-

@article{He2020TheKC,
  title={The Kelmans-Seymour conjecture III: 3-vertices in K4-},
  author={Dawei He and Yan Wang and Xingxing Yu},
  journal={J. Comb. Theory, Ser. B},
  year={2020},
  volume={144},
  pages={265-308}
}
5 Citations

Figures from this paper

4‐Separations in Hajós graphs
As a natural extension of the Four Color Theorem, Hajós conjectured that graphs containing no K5 ‐subdivision are 4‐colorable. Any possible counterexample to this conjecture with minimum number of
Wheels in planar graphs and Hajós graphs
TLDR
If a Hajos graph admits a 4-cut or 5-cut with a planar side then the planarSide must be small or contains a special wheel in the effort to reduce Hajos' conjecture to the Four Color Theorem.
Linking four vertices in graphs of large connectivity
The Kelmans-Seymour conjecture IV: A proof

References

SHOWING 1-10 OF 17 REFERENCES
Non-Separating Paths in 4-Connected Graphs
Abstract.In 1975, Lovász conjectured that for any positive integer k, there exists a minimum positive integer f(k) such that, for any two vertices x, y in any f(k)-connected graph G, there is a path
Nonseparating Cycles in 4-Connected Graphs
We prove that given any fixed edge ra in a 4-connected graph G, there exists a cycle C through ra such that G-(V(C)-{r}) is 2-connected. This will provide the first step in a decomposition for
K5-Subdivisions in graphs containing K-4
A Polynomial Solution to the Undirected Two Paths Problem
TLDR
If G is 4-connected and nonplanar, then such paths P, and P2 exist for any choice of s,, s2, h, and t2 (as conjectured by Watkins).
Graph minors. IX. Disjoint crossed paths
The Kelmans-Seymour conjecture I: Special separations
2-Linked Graphs
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
...
...