Tag Archives: Chromatic number

A model for global compactness

Posted on July 5, 2024 by Assaf Rinot in categories: Compactness, Work In Progress.

Joint work with Sittinon Jirattikansakul and Inbar Oren. Abstract. In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which ℵω+1 carries a uniform ultrafilter that is θ-indecomposable for every uncountable θ<ℵω. In this … Continue reading →

Posted in Compactness, Work In Progress | Tagged , , , | Leave a comment

MFO workshop in Set Theory, February 2017

Posted on February 19, 2017 by Assaf Rinot in categories: Invited Talks.

I gave an invited talk at the Set Theory workshop in Obwerwolfach, February 2017. Talk Title: Coloring vs. Chromatic. Abstract: In a joint work with Chris Lambie-Hanson, we study the interaction between compactness for the chromatic number (of graphs) and … Continue reading →

Posted in Invited Talks | Tagged , , , | Leave a comment

Reflection on the coloring and chromatic numbers

Posted on December 18, 2016 by Assaf Rinot in categories: Compactness, Infinite Graphs, Publications.

Joint work with Chris Lambie-Hanson. Abstract.  We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number.  Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading →

Posted in Compactness, Infinite Graphs, Publications | Tagged , , , , , , , , , , , , , | 2 Comments

Same Graph, Different Universe

Posted on December 13, 2014 by Assaf Rinot in categories: Infinite Graphs, Publications.

Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading →

Posted in Infinite Graphs, Publications | Tagged , , , , , , , | 10 Comments

INFTY Final Conference, March 2014

Posted on February 15, 2014 by Assaf Rinot in categories: Invited Talks.

I gave an invited talk at the INFTY Final Conference meeting, Bonn, March 4-7, 2014. [Curiosity: Georg Cantor was born March 3, 1845] Title: Same Graph, Different Universe. Abstract: In a paper from 1998, answering a question of Hajnal, Soukup … Continue reading →

Posted in Invited Talks | Tagged , , | 1 Comment

Set Theory Programme on Large Cardinals and Forcing, September 2013

Posted on July 19, 2013 by Assaf Rinot in categories: Invited Talks.

I gave an invited talk at the Large Cardinals and Forcing meeting, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, September 23–27, 2013. Talk Title: Hedetniemi’s conjecture for uncountable graphs Abstract: It is proved that in Godel’s constructible universe, for … Continue reading →

Posted in Invited Talks | Tagged , , | 1 Comment

Chromatic numbers of graphs – large gaps

Posted on April 12, 2013 by Assaf Rinot in categories: Compactness, Infinite Graphs, Publications.

Abstract. We say that a graph G is (ℵ0,κ)-chromatic if Chr(G)=κ, while Chr(G′)≤ℵ0 for any subgraph G′ of G of size <|G|. The main result of this paper reads as follows. If  ◻λ+CHλ holds for a given uncountable cardinal λ, … Continue reading →

Posted in Compactness, Infinite Graphs, Publications | Tagged , , , , , , | 6 Comments

The chromatic numbers of the Erdos-Hajnal graphs

Posted on May 4, 2012 by Assaf Rinot in categories: Blog, Expository.

Recall that a coloring c:G→κ of an (undirected) graph (G,E) is said to be chromatic if c(v1)≠c(v2) whenever {v1,v2}∈E. Then, the chromatic number of a graph (G,E) is the least cardinal κ for which there exists a chromatic … Continue reading →

Posted in Blog, Expository | Tagged , , , | 13 Comments