Even-hole-free_graph
Even-hole-free graph
Graph containing no induced cycles with an even number of nodes
In the mathematical area of graph theory, a graph is even-hole-free if it contains no induced cycle with an even number of vertices. More precisely, the definition may allow the graph to have induced cycles of length four, or may also disallow them: the latter is referred to as even-cycle-free graphs.[1]
Addario-Berry et al. (2008) demonstrated that every even-hole-free graph contains a bisimplicial vertex (a vertex whose neighborhood is the union of two cliques), which settled a conjecture by Reed. The proof was later shown to be flawed by Chudnovsky & Seymour (2023), who gave a correct proof.