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Tag Archives: Rado’s conjecture
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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Square principles
Since the birth of Jensen’s original Square principle, many variations of the principle were introduced and intensively studied. Asaf Karagila suggested me today to put some order into all of these principles. Here is a trial. Definition. A square principle … Continue reading
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
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