4 papers
Tolerance Orders of Open and Closed Intervals
Alan Shuchat, Randy Shull, Ann N Trenk
In this paper we combine ideas from tolerance orders with recent work on OC interval orders. We consider representations of posets by unit intervals in which the interval end…
Interval Orders with Two Interval Lengths
Simona Boyadzhiyska, Garth Isaak, Ann N Trenk
A poset has an interval representation if each can be assigned a real interval so that in if and only if lies completely to th…
Finding Balance: Split Graphs and Related Classes
Karen L. Collins, Ann N. Trenk
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Chen…
Split Graphs and Nordhaus-Gaddum Graphs
Christine Cheng, Karen L. Collins, Ann Trenk
A graph G is an NG-graph if χ(G) + χ(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also expl…