Excluding an induced wheel minor in graphs without large induced starsChoi, Mujin (Avtor) Hilaire, Claire (Avtor) Milanič, Martin (Avtor) Wiederrecht, Sebastian (Avtor) induced minorwheeltree-independence numberMaximum Independent SetWe study a conjecture due to Dallard, Krnc, Kwon, Milanič, Munaro, Štorgel, and Wiederrecht stating that for any positive integer d and any planar graph H, the class of all K_{1,d}-free graphs without H as an induced minor has bounded tree-independence number. A k-wheel is the graph obtained from a cycle of length k by adding a vertex adjacent to all vertices of the cycle. We show that the conjecture of Dallard et al. is true when H is a k-wheel for any k at least 3. Our proof uses a generalization of the concept of brambles to tree-independence number. As a consequence of our main result, several important NP-hard problems such as Maximum Independent Set are tractable on K_{1,d}-free graphs without large induced wheel minors. Moreover, for fixed d and k, we provide a polynomial-time algorithm that, given a K_{1,d}-free graph G as input, finds an induced minor model of a k-wheel in G if one exists.20262026-03-25 09:58:25Neznano22851UDK: 519.17ISSN pri članku: 0302-9743OceCobissID: 272877059DOI: 10.1007/978-3-032-11835-6_10COBISS.SI-ID: 272882435sl