Reducing Hajós' 4-coloring conjecture to 4-connected graphs

Authors:
Xingxing Yu;Florian Zickfeld
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA and Center for Combinatorics, LPMC, Nankai University, Tianjin, China;School of Mathematics, Georgia Institute of Technology, Atlanta, GA
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 3
Cited 2

Do 3n−5 edges force a subdivision of K5?

Journal of Graph Theory
Topological minors in graphs of large girth

Journal of Combinatorial Theory Series B
Some remarks on Hajós' conjecture

Journal of Combinatorial Theory Series B

Hajós' conjecture and cycle power graphs

European Journal of Combinatorics
Independent paths and K5-subdivisions

Journal of Combinatorial Theory Series B

Quantified Score

Hi-index	0.00

Visualization

Abstract

Hajós conjectured that, for any positive integer k, every graph containing no Kk+1-subdivision is k-colorable. This is true when k ≤ 3, and false when k ≥ 6. Hajós' conjecture remains open for k = 4, 5. In this paper, we show that any possible counterexample to this conjecture for k = 4 with minimum number of vertices must be 4-connected. This is a step in an attempt to reduce Hajós' conjecture for k = 4 to the conjecture of Seymour that any 5-connected non-planar graph contains a K5-subdivision.