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- W3130147429 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 $K_{chi(G)}$ 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 $alpha(G)ge 2$ and no hole of length between $4$ and $2alpha(G)$ satisfies this conjecture. In particular, every $C_4$-free graph $G$ with $alpha(G)= 2$ 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 $|V(H)|le 4$. If $G$ is $H$-free, then $G$ satisfies the Lescure-Meyniel conjecture." @default.
- W3130147429 created "2021-03-01" @default.
- W3130147429 creator A5084351080 @default.
- W3130147429 date "2020-04-11" @default.
- W3130147429 modified "2023-09-27" @default.
- W3130147429 title "Clique immersions in graphs of independence number two with certain forbidden subgraphs" @default.
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