Yusuf Civan

Castelnuovo-Mumford Regularity of Graphs

We present new combinatorial insights into the calculation of (Castelnuovo-Mumford) regularity of graphs.

Upper Maximal Graphs of Posets

We introduce and study a class of simple graphs, the upper-maximal graphs (UM-graphs), associated to finite posets. The vertices of the UM-graph of a given poset P are the elements of P, and edges are formed by those vertices x and y whenever any maximal element of P that is greater than x is also greater than y or vise versa. We show that the class of UM-graphs constitutes a subclass of comparability graphs. We further provide a characterization of chordal UM-graphs, and compare UM-graphs with known bound graphs of posets.

Stably and almost complex structures on bounded flag manifolds

We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring Ω U * .