Bustamante, SebastiánQuiroz, Daniel A.Stein, MayaZamora, José2023-04-112023-04-112022-12European Journal of CombinatoricsOpen AccessVolume 106December 2022 Article number 1035500195-6698https://repositorio.unab.cl/xmlui/handle/ria/48451Indexación: Scopus.The 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. © 2022enHadwiger's ConjectureConnected GraphGraphArtículoAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)10.1016/j.ejc.2022.103550