Abstract. We say that a graph
The main result of this paper reads as follows.
If
We also study
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Citation information:
A. Rinot, Chromatic numbers of graphs – large gaps, Combinatorica, 35(2): 215-233, 2015.
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Successor of Regular Cardinal Was Ulam right? Subtle tree property Diamond Axiom R Chromatic number Antichain Commutative projection system Cohen real Universal Sequences square GMA higher Baire space unbounded function Poset ccc L-space xbox Generalized descriptive set theory strongly bounded groups sap Prikry-type forcing projective Boolean algebra Hereditarily Lindelöf space Cardinal Invariants Minimal Walks Hindman's Theorem Ostaszewski square Amenable C-sequence Martin's Axiom Respecting tree SNR Precaliber Rainbow sets Foundations indecomposable ultrafilter Ascent Path Strongly Luzin set Luzin set PFA free Souslin tree Small forcing Slim tree Closed coloring specializable Souslin tree incompactness Mandelbrot set nonmeager set Almost Souslin Reflecting stationary set Shelah's Strong Hypothesis PFA(S)[S] Subadditive stationary hitting Jonsson cardinal free Boolean algebra coloring number Singular cofinality Dowker space Forcing Axioms polarized partition relation full tree Fast club Countryman line Forcing Chang's conjecture Ulam matrix Vanishing levels O-space Prevalent singular cardinals square principles Intersection model Sakurai's Bell inequality Almost-disjoint family transformations b-scale ZFC construction reflection principles Singular Density Weakly compact cardinal approachability ideal weak diamond middle diamond P-Ideal Dichotomy weak square regressive Souslin tree Iterated forcing Aronszajn tree Square-Brackets Partition Relations countably metacompact Non-saturation OCA Reduced Power diamond star Partition Relations very good scale AIM forcing stationary reflection Greatly Mahlo Nonspecial tree S-Space Ramsey theory over partitions Uniformization Ineffable cardinal HOD Sierpinski's onto mapping principle tensor product graph Open Access Strong coloring Rock n' Roll positive partition relation Local Club Condensation. Sigma-Prikry Knaster and friends Subnormal ideal Generalized Clubs Almost countably chromatic Diamond for trees Fat stationary set stick Commutative cancellative semigroups Selective Ultrafilter club_AD Parameterized proxy principle Knaster Fodor-type reflection Analytic sets Strongly compact cardinal Erdos Cardinal Distributive tree Club Guessing Coherent tree 54G20 super-Souslin tree Constructible Universe Well-behaved magma Cardinal function Successor of Singular Cardinal Whitehead Problem Uniformly homogeneous C-sequence Microscopic Approach Hedetniemi's conjecture Dushnik-Miller Singular cardinals combinatorics Large Cardinals Erdos-Hajnal graphs Souslin Tree Uniformly coherent Absoluteness Lipschitz reduction Subtle cardinal Filter reflection Postprocessing function weak Kurepa tree Rado's conjecture Diamond-sharp Kurepa Hypothesis
That really is a simple method! Nice one Assaf!
Thank you very much!!
Submitted to Combinatorica, January 2013.
Accepted, April 2013.
Hi Assaf. It is a nice paper! (By the way, none of the references I looked at had anything as detailed as your results on changing chromatic numbers.)
Thanks a lot for checking!
p.s.
In addition to the results I told you about, I found more, including a ZFC example of an uncountably chromatic graph that can be made countably chromatic via a c.c.c. forcing, and that GCH entails analogous statements for successors of regulars above
It turns out there is no need for a nonreflecting stationary set!
In an upcoming paper with Chris Lambie-Hanson, we shall show that moreover the existence of an almost countably chromatic graph of size and chromatic number