| Title: | Excluding an induced wheel minor in graphs without large induced stars |
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| Authors: | ID Choi, Mujin (Author)
ID Hilaire, Claire (Author)
ID Milanič, Martin (Author)
ID Wiederrecht, Sebastian (Author) |
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| Files: |  https://arxiv.org/abs/2506.08829
https://link.springer.com/chapter/10.1007/978-3-032-11835-6_10
 RAZ_Choi_Mujin_2026.pdf (410,19 KB, This file will be accessible after 01.01.2027)
MD5: 5A6F5D1AE81D14AF440B21DD35847C71
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | We 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. |
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| Keywords: | induced minor, wheel, tree-independence number, Maximum Independent Set |
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| Publication version: | Version of Record |
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| Year of publishing: | 2026 |
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| Number of pages: | Str. 135-148 |
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| PID: | 20.500.12556/RUP-22851  |
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| UDC: | 519.17 |
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| ISSN on article: | 0302-9743 |
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| DOI: | 10.1007/978-3-032-11835-6_10 |
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| COBISS.SI-ID: | 272882435 |
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| Publication date in RUP: | 25.03.2026 |
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| Views: | 73 |
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| Downloads: | 2 |
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