Quiroz, Daniel A.2022-11-302022-11-302021http://repositoriobibliotecas.uv.cl/handle/uvscl/7506The Lescure–Meyniel conjecture is the analogue of Hadwiger’s conjecture for the immersion order. It states that every graph contains the complete graph as an immersion, and like its minor-order counterpart it is open even for graphs with independence number 2. We show that every graph with independence number and no hole of length between 4 and satisfies this conjecture. In particular, every -free graph with satisfies the Lescure–Meyniel conjecture. We give another generalisation of this corollary, as follows. Let and be graphs with independence number at most 2, such that . If is -free, then satisfies the Lescure–Meyniel conjecture.GRAPH IMMERSIONINDEPENDENCE NUMBERFORBIDDEN SUBGRAPHSCHROMATIC NUMBERHADWIGER’S CONJECTURECLIQUEArticulohttps://doi.org/10.1016/j.disc.2021.112365