Sintiari and Trotignon's diamond conjecture for even-hole-free graphs

Let a diamond be the graph obtained from a two-edge path by adding a universal vertex. Consider graphs with no induced even hole and no induced $K_4$.

Sintiari and Trotignon's conjecture. Every (even-hole, $K_4$)-free graph of sufficiently large treewidth contains a diamond as an induced subgraph.

This conjecture was posed because the graphs in the paper's construction have many induced diamonds. It is solved by the paper's main theorem, which proves the stronger characterization that a graph $H$ occurs in every sufficiently large-treewidth (even-hole, $K_4$)-free graph exactly when $H$ is a $K_4$-free chordal graph.