Hajnal-Máté graphs, Cohen reals, and disjoint-type guessing
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586662" target="_blank" >RIV/67985840:_____/24:00586662 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/mtk.12261" target="_blank" >https://doi.org/10.1112/mtk.12261</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/mtk.12261" target="_blank" >10.1112/mtk.12261</a>
Alternative languages
Result language
angličtina
Original language name
Hajnal-Máté graphs, Cohen reals, and disjoint-type guessing
Original language description
A Hajnal-Máté graph is an uncountably chromatic graph on (Formula presented.) satisfying a certain natural sparseness condition. We investigate Hajnal–Máté graphs and generalizations thereof, focusing on the existence of Hajnal-Máté graphs in models resulting from adding a single Cohen real. In particular, answering a question of Dániel Soukup, we show that such models necessarily contain triangle-free Hajnal-Máté graphs. In the process, we isolate a weakening of club guessing called disjoint-type guessing that we feel is of interest in its own right. We show that disjoint-type guessing is independent of (Formula presented.) and, if disjoint-type guessing holds in the ground model, then the forcing extension by a single Cohen real contains Hajnal-Máté graphs (Formula presented.) such that the chromatic numbers of finite subgraphs of (Formula presented.) grow arbitrarily slowly.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-04683S" target="_blank" >GA23-04683S: Compactness in set theory, with applications to algebra and graph theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematika
ISSN
0025-5793
e-ISSN
2041-7942
Volume of the periodical
70
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
e12261
UT code for WoS article
001233559900001
EID of the result in the Scopus database
2-s2.0-85194549575