3 problems

A finite poset has dimension $d$ when its order is the intersection of $d$ linear orders. Its Hasse diagram is the graph of the poset's cover relations, and the independence number…

A finite poset has dimension $d$ when $d$ is the least number of linear orders whose intersection is the poset order. Its Hasse diagram is the graph whose vertices are the poset el…

Let $G$ be a Hasse diagram on $n$ vertices, and let $\chi(G)$ denote its chromatic number. Hasse-diagram chromatic number gap conjecture. There exists $\epsilon>0$ such that … The…