Tree-width dichotomy
Vadim Lozin, Igor Razgon · European Journal of Combinatorics · 2022
We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a tripod.