Almost all Steiner triple systems are almost resolvable

Asaf Ferber; Matthew Kwan

Almost all Steiner triple systems are almost resolvable

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arxiv 1907.06744 v2 pith:2DVHPNKD submitted 2019-07-15 math.CO

Asaf Ferber , Matthew Kwan This is my paper · ORCID

classification math.CO

keywords almoststeinersystemstripleresolvableadmitdecompositiondisjoint

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We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).

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Large monochromatic components in 3-edge-colored Steiner triple systems
math.CO 2019-08 conditional novelty 7.0 of 10

For almost all Steiner triple systems on n vertices, every 3-edge-coloring has a monochromatic component on (1-o(1))n vertices.

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