Motwani

Removing bottlenecks in the recognition of small $(k,\ell)$-graph classes

arXiv:2510.17665v2 Announce Type: replace Abstract: A graph is a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. This family simultaneously generalizes split, bipartite, and co-bipartite graphs. While the recognition problem is NP-complete whenever $k\geq 3$ or $\ell\geq 3$, the remaining small cases are polynomial-time solvable.