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Ramsey theory on Steiner triples
Author(s) -
Granath Elliot,
Gyárfás András,
Hardee Jerry,
Watson Trent,
Wu Xiaoze
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21585
Subject(s) - combinatorics , steiner system , mathematics , block (permutation group theory) , monochromatic color , point (geometry) , discrete mathematics , ramsey theory , geometry , physics , optics
We call a partial Steiner triple system C (configuration) t ‐Ramsey if for large enough n (in terms of C , t ), in every t ‐coloring of the blocks of any Steiner triple system STS( n ) there is a monochromatic copy of C . We prove that configuration C is t ‐Ramsey for every t in three cases: C is acyclic every block of C has a point of degree one C has a triangle with blocks 123, 345, 561 with some further blocks attached at points 1 and 4 This implies that we can decide for all but one configurations with at most four blocks whether they are t ‐Ramsey. The one in doubt is the sail with blocks 123, 345, 561, 147.