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nonmeager set tensor product graph Diamond Jonsson cardinal Selective Ultrafilter Cardinal Invariants Souslin Tree Subtle cardinal Diamond-sharp Rainbow sets Lipschitz reduction Large Cardinals regressive Souslin tree Sierpinski's onto mapping principle Diamond for trees Uniformization middle diamond 54G20 Uniformly homogeneous Postprocessing function specializable Souslin tree Monotonically far Forcing Small forcing stationary hitting diamond star Luzin set Microscopic Approach very good scale free Souslin tree super-Souslin tree Prikry-type forcing Strongly Luzin set strongly bounded groups Entangled linear order Reduced Power Weakly compact cardinal C-sequence Dushnik-Miller Forcing with side conditions Was Ulam right? Amenable C-sequence Commutative projection system Fast club Reflecting stationary set Uniformly coherent ZFC construction Cardinal function HOD indecomposable filter P-Ideal Dichotomy coloring number Commutative cancellative semigroups Hindman's Theorem Forcing Axioms Subadditive Successor of Regular Cardinal Aronszajn tree Vanishing levels Martin's Axiom approachability ideal Kurepa Hypothesis AIM forcing Chang's conjecture Strong coloring square Shelah's Strong Hypothesis transformations Poset Absoluteness Subnormal ideal Ulam matrix GMA Hedetniemi's conjecture Non-saturation Generalized descriptive set theory Universal Sequences Nonspecial tree Hereditarily Lindelöf space Intersection model Respecting tree sap polarized partition relation stationary reflection ccc Strongly compact cardinal Almost Souslin Singular Density unbounded function PFA(S)[S] Knaster weak square O-space Erdos Cardinal Well-behaved magma Ramsey theory over partitions Parameterized proxy principle Distributive tree Countryman line Fodor-type reflection Local Club Condensation. stick Open Access Square-Brackets Partition Relations Generalized Clubs Subtle tree property incompactness b-scale weak diamond reflection principles S-Space Fat stationary set square principles Rock n' Roll positive partition relation Whitehead Problem SNR Antichain Almost-disjoint family Singular cofinality projective Boolean algebra Slim tree higher Baire space Ostaszewski square Partition Relations Filter reflection Mandelbrot set Foundations free Boolean algebra Minimal Walks Almost countably chromatic Rado's conjecture Analytic sets Iterated forcing Cohen real Precaliber Sigma-Prikry Sakurai's Bell inequality Interval topology on trees weak Kurepa tree Knaster and friends Prevalent singular cardinals Coherent tree PFA Ascent Path Ascending path xbox Axiom R Greatly Mahlo L-space Erdos-Hajnal graphs perfectly normal Chromatic number full tree Constructible Universe Successor of Singular Cardinal Closed coloring OCA countably metacompact club_AD Singular cardinals combinatorics Ineffable cardinal Dowker space Club Guessing
Tag Archives: 05C63
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
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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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
Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading
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
