5 Citations
4‐Separations in Hajós graphs
- MathematicsJ. Graph Theory
- 2022
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
- MathematicsJ. Graph Theory
- 2021
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.
References
SHOWING 1-10 OF 17 REFERENCES
Non-Separating Paths in 4-Connected Graphs
- Mathematics
- 2005
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
- MathematicsSIAM J. Discret. Math.
- 2003
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…
A Polynomial Solution to the Undirected Two Paths Problem
- MathematicsJACM
- 1980
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).