The origin of many quantum-material phenomena is intimately related to the presence flat electronic bands. In quantum simulation, such bands have been realized through line-graph lattices, a class lattices known exhibit Based on that work, we conduct high-throughput screening for among crystalline structures Materials Flatband Database and report new candidates materials lattice models. particu...

We determine the exact treewidth of the line graph of the complete graph. More generally, we determine the exact treewidth of the line graph of a regular complete multipartite graph. For an arbitrary complete multipartite graph, we determine the treewidth of the line graph up to a lower order term.