The uncountable Hadwiger conjecture and characterizations of trees using graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00584366" target="_blank" >RIV/67985840:_____/24:00584366 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s10474-024-01399-x" target="_blank" >https://doi.org/10.1007/s10474-024-01399-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10474-024-01399-x" target="_blank" >10.1007/s10474-024-01399-x</a>

Result language

angličtina

Original language name

The uncountable Hadwiger conjecture and characterizations of trees using graphs

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Acta Mathematica Hungarica

ISSN

0236-5294

e-ISSN

1588-2632

Volume of the periodical

172

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

15

Pages from-to

19-33

UT code for WoS article

001154647900005

EID of the result in the Scopus database

2-s2.0-85183731803