Tag Archives: Almost countably chromatic

Hedetniemi’s conjecture for uncountable graphs

Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal κ, there exist graphs G and H of size and chromatic number κ, for which the tensor product graph G×H is countably chromatic. … Continue reading

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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

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Chromatic numbers of graphs – large gaps

Abstract. We say that a graph G is (0,κ)-chromatic if Chr(G)=κ, while Chr(G)0 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

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