A strongly non-Ramsey uncountable graph

Péter Komjáth

Fundamenta Mathematicae (1997)

  • Volume: 154, Issue: 2, page 203-205
  • ISSN: 0016-2736

Abstract

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It is consistent that there exists a graph X of cardinality ℵ 1 such that every graph has an edge coloring with ℵ 1 colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).

How to cite

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Komjáth, Péter. "A strongly non-Ramsey uncountable graph." Fundamenta Mathematicae 154.2 (1997): 203-205. <http://eudml.org/doc/212234>.

@article{Komjáth1997,
abstract = {It is consistent that there exists a graph X of cardinality $ℵ_1$ such that every graph has an edge coloring with $ℵ_1$ colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).},
author = {Komjáth, Péter},
journal = {Fundamenta Mathematicae},
keywords = {Ramsey theorem; graph coloring; forcing notion; consistency; Todorčević function},
language = {eng},
number = {2},
pages = {203-205},
title = {A strongly non-Ramsey uncountable graph},
url = {http://eudml.org/doc/212234},
volume = {154},
year = {1997},
}

TY - JOUR
AU - Komjáth, Péter
TI - A strongly non-Ramsey uncountable graph
JO - Fundamenta Mathematicae
PY - 1997
VL - 154
IS - 2
SP - 203
EP - 205
AB - It is consistent that there exists a graph X of cardinality $ℵ_1$ such that every graph has an edge coloring with $ℵ_1$ colors in which the induced copies of X (if there are any) are totally multicolored (get all possible colors).
LA - eng
KW - Ramsey theorem; graph coloring; forcing notion; consistency; Todorčević function
UR - http://eudml.org/doc/212234
ER -

References

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  1. [1] P. Erdős, A. Hajnal, A. Máté and R. Rado, Combinatorial Set Theory: Partition Relation for Cardinals, North-Holland, 1984. Zbl0573.03019
  2. [2] A. Hajnal and P. Komjáth, Embedding graphs into colored graphs, Trans. Amer. Math. Soc. 307 (1988), 395-409; corrigendum: 332 (1992), 475. Zbl0659.03029
  3. [3] S. Shelah, Consistency of positive partition theorems for graphs and models, in: Set Theory and Applications, J. Steprāns and S. Watson (eds.), Lecture Notes in Math. 1401, Springer, 1989, 167-193. 
  4. [4] S. Todorčević, Coloring pairs of countable ordinals, Acta Math. 159 (1987), 261-294. Zbl0658.03028

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