Sebastián BustamanteQuiroz, DanielDanielQuirozMaya SteinJosé Zamora2025-12-062025-12-062022-12-0110.1016/j.ejc.2022.1035502-s2.0-85136695345https://cris-uv-2.scimago.es/handle/123456789/7128WOS:000861270900001The analogue of Hadwiger's conjecture for the immersion order states that every graph G contains Kχ(G) as an immersion. If true, this would imply that every graph with n vertices and independence number α contains K⌈[Formula presented]⌉ as an immersion. The best currently known bound for this conjecture is due to Gauthier, Le and Wollan, who recently proved that every graph G contains an immersion of a clique on ⌈[Formula presented]⌉ vertices. Their result implies that every n-vertex graph with independence number α contains an immersion of a clique on ⌈[Formula presented]−1.13⌉ vertices. We improve on this result for all α≥3, by showing that every n-vertex graph with independence number α≥3 contains an immersion of a clique on ⌊[Formula presented]⌋−1 vertices, where f is a nonnegative function.enacceso abiertoComputational Theory And MathematicsDiscrete Mathematics And CombinatoricsGeometry And TopologyMathematicsTheoretical Computer Sciencearticle