z-logo
Premium
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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here