(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.
Hujter and Lángi defined the k-fold Borsuk number of a set S in Euclidean n-space of diameter d > 0 as the smallest cardinality of a family F of subsets of S, of diameters strictly less than d, such that every point of S belongs to at least k members of F.
We investigate whether a k-fold Borsuk covering of a set S in a finite dimensional real normed space can be extended to a completion of S. Furthermore, we determine the k-fold Borsuk number of sets in not angled normed planes, and give a partial characterization for sets in angled planes.
strains Organic acids production (µg mL −1 ) Acetate Lactate Butyrate K4E (5.86 ± 0.04) c (16.43 ± 0.70) d (0.122 ± 0.002) g,h K7 (5.77 ± 0.05) c (15.78 ± 0.37) d (0.163 ± 0.002) h K16 (5.18 ± 0.02) b (11.46 ± 0.04) e (0.090 ± 0.001) g RD7 (4.07 ± 0.03) a