A width parameter useful for chordal and co-comparability graphs

We generalize these ideas to bigger graph classes. We introduce a new width parameter sim-width, of stronger modeling power than mim-width, by making a small change in the definition of mim-width. We prove that chordal graphs and co-comparability graphs have sim-width at most 1. We investigate a way to bound mim-width for graphs of bounded sim-width by excluding Kt⊟Kt and Kt⊟St as induced minors or induced subgraphs, and give algorithmic consequences. Lastly, we show that circle graphs have unbounded sim-width, and thus also unbounded mim-width.