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- W3138725079 abstract "The Lescure–Meyniel conjecture is the analogue of Hadwiger’s conjecture for the immersion order. It states that every graph G contains the complete graph Kχ(G) as an immersion, and like its minor-order counterpart it is open even for graphs with independence number 2. We show that every graph G with independence number α(G)≥2 and no hole of length between 4 and 2α(G) satisfies this conjecture. In particular, every C4-free graph G with α(G)=2 satisfies the Lescure–Meyniel conjecture. We give another generalisation of this corollary, as follows. Let G and H be graphs with independence number at most 2, such that |V(H)|≤4. If G is H-free, then G satisfies the Lescure–Meyniel conjecture." @default.
- W3138725079 created "2021-03-29" @default.
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- W3138725079 date "2021-06-01" @default.
- W3138725079 modified "2023-09-27" @default.
- W3138725079 title "Clique immersions in graphs of independence number two with certain forbidden subgraphs" @default.
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- W3138725079 doi "https://doi.org/10.1016/j.disc.2021.112365" @default.
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