Coloring BIBDs with block size 4

Abstract

It is shown that for each integer m ≥ 1 there exists a lower bound, vm, with the property that for all v ≥ vm with v ≡ 1, 4 (mod 12) there exists an m‐chromatic S(2, 4, v) design. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 403–409, 1998

On list coloring Steiner triple systems

“…They note in particular that the STS constructed by Bose [4] and Skolem [17] for all admissible orders have chromatic number 3. On the other hand, de Brandes et al [7] showed that for each k ≥ 3, there exists an STS(n) of chromatic number k for every sufficiently large admissible n. In terms of general upper bounds, Phelps and Rödl [15] proved that there exists a constant C such that the chromatic number of any STS(n) is at most C n/ log n. Similar problems for other classes of designs have been studied as well, for example Linek and Wantland [12] proved a result analogous to [7] for BIBD's with block size four.…”