The uncountable Hadwiger conjecture and characterizations of trees using graphs

0584366 - MÚ 2025 RIV DE eng J - Journal Article
Uhrik, Dávid
The uncountable Hadwiger conjecture and characterizations of trees using graphs.
Acta Mathematica Hungarica. Roč. 172, č. 1 (2024), s. 19-33. ISSN 0236-5294. E-ISSN 1588-2632
Institutional support: RVO:67985840
Keywords : uncountable Hadwiger conjecture * special tree * Suslin tree * uncountable graphs
OECD category: Pure mathematics
Impact factor: 0.9, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s10474-024-01399-x

We prove that the existence of a non-special tree of size λ is equivalent to the existence of an uncountably chromatic graph with no Kω1 minor of size λ, establishing a connection between the special tree number and the uncountable Hadwiger conjecture. Also characterizations of Aronszajn, Kurepa and Suslin trees using graphs are deduced. A new generalized notion of connectedness for graphs is introduced using which we are able to characterize weakly compact cardinals.
Permanent Link: https://hdl.handle.net/11104/0352285