(Theta, triangle)‐free and (even hole, K4)‐free graphs—Part 1: Layered wheels
Ni Luh Dewi Sintiari, Nicolas Trotignon · Journal of Graph Theory · 2021
Abstract We present a construction called layered wheel. Layered wheels are graphs of arbitrarily large treewidth and girth. They might be an outcome for a possible theorem characterizing graphs with large treewidth in terms of their induced subgraphs (while such a characterization is well‐understood in terms of minors). They also provide examples of graphs of large treewidth and large rankwidth in well‐studied classes, such as (theta, triangle)‐free graphs and even‐hole‐free graphs with no (where a hole is a chordless cycle of length at least four, a theta is a graph made of three internally vertex disjoint paths of length at least two linking two vertices, and is the complete graph on four vertices).