Ramsey Numbers for Partially-Ordered Sets

Ramsey Numbers for Partially-Ordered Sets

We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We e...

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Veröffentlicht in:Order (Dordrecht) 2018-11, Vol.35 (3), p.557-579
Hauptverfasser: Cox, Christopher, Stolee, Derrick
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Boolean algebra
Discrete Mathematics
Graphs
Lattices
Mathematics
Mathematics and Statistics
Numbers
Order
Ordered Algebraic Structures
Software reviews
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creator Cox, Christopher
Stolee, Derrick
description We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey numbers. We formalize situations in which we can use arbitrary families of partially-ordered sets to form host graphs for Ramsey problems. We explore connections to well studied Turán-type problems in partially-ordered sets, particularly those in the Boolean lattice. We find a strong difference between Ramsey numbers on the Boolean lattice and ordered Ramsey numbers when the partial ordering on the graphs have large antichains.
doi_str_mv 10.1007/s11083-017-9449-9
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subjects Algebra
Boolean algebra
Discrete Mathematics
Graphs
Lattices
Mathematics
Mathematics and Statistics
Numbers
Order
Ordered Algebraic Structures
Software reviews
title Ramsey Numbers for Partially-Ordered Sets
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