20.500.12556/RUP-22210 Induced minor models Structural properties and algorithmic consequences A graph H is an induced minor of G if there exists an induced minor model of H in G, that is, a collection of pairwise disjoint subsets of vertices of G labeled by the vertices of H, each inducing a connected subgraph in G, such that two vertices of H are adjacent if and only if there is an edge in G between the corresponding subsets. In this paper, we investigate structural properties of induced minor models, including bounds on treewidth and chromatic number of the subgraphs induced by minimal induced minor models. As algorithmic applications of our structural results, we make use of recent developments regarding tree-independence number to show that if H is the 4-wheel, the 5-vertex complete graph minus an edge, or a complete bipartite graph K2,q , then there is a polynomial-time algorithm to find in a given graph G an induced minor model of H in G, if there is one. We also develop an alternative polynomial-time algorithm for recognizing graphs that do not contain K2,3 as an induced minor, which revolves around the idea of detecting the induced subgraphs whose presence is forced when the input graph contains K2,3 as an induced minor. It turns out that all these induced subgraphs are Truemper configurations. induced minor treewidth chromatic number tree-independence number Truemper configuration induciran minor drevesna širina kromatično število drevesno neodvisnostno število Truemperjeva konfiguracija true false true Angleški jezik Slovenski jezik Članek v reviji 2025-12-16 14:10:26 2025-12-16 14:10:27 2025-12-19 03:04:37 0000-00-00 00:00:00 2026 0 0 str. 1-19 article 103738 Vol. 157 May 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-12-02 519.17 0022-0000 10.1016/j.jcss.2025.103738 261704195 RAZ_Bousquet_Nicolas_2026.pdf RAZ_Bousquet_Nicolas_2026.pdf 1 5056A3991347B1384B05F2839CBD14B1 364ec44d9c4cb6ad87729cebccd47f326756ef934a788c4056fa3829a647fdb4 0acdcc6f-da81-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32243 https://www.sciencedirect.com/science/article/pii/S0022000025001205?via%3Dihub 1 e482eb58-da80-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32242 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Inštitut Andrej Marušič 0 0 0