2015/12/16 by Cox, Christopher, Stolee, Derrick · 1 citation
#05C55 #06A07 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1512.05261
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.