Crossing Minimization for 1-page and 2-page Drawings of Graphs with Bounded Treewidth

Abstract

We investigate crossing minimization for $1$-page and $2$-page book drawings. We show that computing the $1$-page crossing number is fixed-parameter tractable with respect to the number of crossings, that testing $2$-page planarity is fixed-parameter tractable with respect to treewidth, and that computing the $2$-page crossing number is fixed-parameter tractable with respect to the sum of the number of crossings and the treewidth of the input graph. We prove these results via Courcelle's theorem on the fixed-parameter tractability of properties expressible in monadic second order logic for graphs of bounded treewidth.