Forbidden obstructions for interval k-graphs

Characterize the forbidden obstructions for interval k-graphs, including the obstructions arising when k=2.

Background

The paper characterizes interval k-graphs using vertex orderings that avoid specified colored forbidden patterns and develops a recognition algorithm based on an auxiliary pair-digraph. It also discusses known obstruction families for interval bigraphs, which are the case k=2, including exobicliques and additional obstructions that cannot be captured by a finite number of families.

For general interval k-graphs, especially when k>2, the paper exhibits new obstruction examples but does not provide a complete characterization. The unresolved problem is to identify all forbidden obstructions; the paper observes that systematic enumeration may nevertheless be possible.