(the unique system consisting of two triples on four vertices). This class contains all odd circuits of length ≧ 7. We also
show that consistently there are two finite triple systems such that they can separately be omitted by uncountably chromatic
triple systems but not both.
We investigate the chromatic number of infinite graphs whose definition is motivated by the theorem of Engelking and Karłowicz
(in [?]). In these graphs, the vertices are subsets of an ordinal, and two subsets X and Y are connected iff for some a ∈ X ∩ Y the order-type of a ∩ X is different from that of a ∩ Y.
In addition to the chromatic number x(G) of these graphs we study χκ(G), the κ-chromatic number, which is the least cardinal µ with a decomposition of the vertices into µ classes none of which contains
a κ-complete subgraph.
János Gerlits died unexpectedly in 2008. In this paper we attempt to make a small tribute to his very powerful mathematical legacy by describing the emerging impact of two ideas, γ-spaces and Gerlits-Nagy spaces, from  and .