Detecting $K_2,3$ as an induced minor
<|reference_start|>Detecting $K_2,3$ as an induced minor: We consider a natural generalization of chordal graphs, in which every minimal separator induces a subgraph with independence number at most $2$. Such graphs can be equivalently defined as graphs that do not contain the complete bipartite graph $K_{2,3}$ as an induced minor, that is, graphs from which $K_{2,3}$ cannot be obtained by a sequence of edge contractions and vertex deletions.   We develop a polynomial-time algorithm for recognizing these graphs. Our algorithm relies on a characterization of $K_{2,3}$-induced minor-free graphs in terms of excluding particular induced subgraphs, called Truemper configurations.<|reference_end|>
@article{dallard2024detecting,
    title={Detecting $K_{2,3}$ as an induced minor},
    author={Cl'ement Dallard, Ma"el Dumas, Claire Hilaire, Martin Milaniv{c},
  Anthony Perez, and Nicolas Trotignon},
    journal={arXiv preprint arXiv:2402.08332},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08332},
    primaryClass={math.CO cs.DM cs.DS}
}