Dimension for Posets and Chromatic Number for Graphs
William T. Trotter · 2019
In this chapter, the authors survey three important research themes involving dimension for partially ordered sets (posets). In each case, there are analogous results involving chromatic number for graphs. These themes have been chosen to highlight recent research on the combinatorics of posets and to illustrate the broad range of connections with other areas of combinatorial mathematics. The authors outline proofs for these results, and this approach yields a number of good exercises for students. They also include comments on open problems for future research. Readers who are completely new to the subject of combinatorics on posets may find additional information in the author’s monograph and survey article. The authors have only scratched the surface of interesting and important problems linking the dimension of posets with graph theoretic properties of cover graphs.