### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014

### Keywords

Diamond b-scale weak square Universal Sequences Generalized Clubs Luzin set coloring number Absoluteness Constructible Universe super-Souslin tree Almost-disjoint famiy P-Ideal Dichotomy Parameterized proxy principle Weakly compact cardinal Chromatic number very good scale 11P99 Prevalent singular cardinals Erdos-Hajnal graphs xbox Hereditarily Lindelöf space Shelah's Strong Hypothesis Cardinal function Mandelbrot set Aronszajn tree Forcing Axioms Uniformization free Souslin tree Antichain 05A17 Axiom R Souslin Tree middle diamond sap polarized partition relation Fast club S-Space Almost Souslin Non-saturation Slim tree Chang's conjecture OCA Singular cardinals combinatorics Hedetniemi's conjecture PFA Prikry-type forcing Large Cardinals Rock n' Roll weak diamond Square-Brackets Partition Relations L-space Cohen real Ostaszewski square HOD Minimal Walks Selective Ultrafilter Foundations Ascent Path Rado's conjecture Hindman's Theorem Stevo Todorcevic Dushnik-Miller Rainbow sets Coherent tree approachability ideal incompactness Postprocessing function Distributive tree Successor of Singular Cardinal free Boolean algebra Fat stationary set Nonspecial tree diamond star Small forcing Club Guessing Successor of Regular Cardinal ccc Kurepa Hypothesis PFA(S)[S] Microscopic Approach reflection principles projective Boolean algebra square Almost countably chromatic Sakurai's Bell inequality specializable Souslin tree Erdos Cardinal tensor product graph Partition Relations Poset Martin's Axiom Commutative cancellative semigroups Uniformly coherent Cardinal Invariants square principles Singular Density Fodor-type reflection stationary reflection Whitehead Problem Forcing Singular coﬁnality Reduced Power Knaster Jonsson cardinal stationary hitting

# Tag Archives: Chromatic number

## MFO workshop in Set Theory, February 2017

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 Chromatic number, coloring number, incompactness, stationary reflection
Leave a comment

## Reflection on the coloring and chromatic numbers

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

## Same Graph, Different Universe

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 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments

## INFTY Final Conference, March 2014

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

## Set Theory Programme on Large Cardinals and Forcing, September 2013

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 Almost countably chromatic, Chromatic number, Hedetniemi's conjecture
1 Comment

## Chromatic numbers of graphs – large gaps

Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading

Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
6 Comments

## The chromatic numbers of the Erdos-Hajnal graphs

Recall that a coloring $c:G\rightarrow\kappa$ of an (undirected) graph $(G,E)$ is said to be chromatic if $c(v_1)\neq c(v_2)$ whenever $\{v_1,v_2\}\in E$. Then, the chromatic number of a graph $(G,E)$ is the least cardinal $\kappa$ for which there exists a chromatic … Continue reading

Posted in Blog, Expository
Tagged Chromatic number, Erdos-Hajnal graphs, Rado's conjecture, reflection principles
11 Comments