The even-hole-free 3-divisibility conjecture

A graph with at least one edge is $k$-divisible if the vertex set of each induced subgraph with at least one edge can be partitioned into $k$ sets, none of which contains a largest clique of that induced subgraph. An even hole is a chordless cycle of even length at least four.

Even-hole-free 3-divisibility conjecture. Every even-hole-free graph is 3-divisible.

This extends the paper's discussion of divisibility for even-hole-free graphs. The conjecture remains open.