Csaba Biró

Posets with Cover Graph of Pathwidth two have Bounded Dimension

Joret, Micek, Milans, Trotter, Walczak, and Wang recently asked if there exists a constant d such that if P is a poset with cover graph of P of pathwidth at most 2, then dim(P)=d. We answer this question in the affirmative by showing that d=17 is sufficient. We also show that if P is a poset containing the standard example S5 as a subposet, then the cover graph of P has treewidth at least 3.

Forcing Posets with Large Dimension to Contain Large Standard Examples

The dimension of a poset P, denoted

Standard Examples as Subposets of Posets

\dim (P)

The rate of growth of the minimum clique size of graphs of given order and chromatic number

dim(P), is the least positive integer d for which P is the intersection of d linear extensions of P. The maximum dimension of a poset P with

Large Chromatic Number and Ramsey Graphs

|P|\le 2n+1

Large standard examples in posets with high dimension and fractional dimension

|P|≤2n+1 is n, provided