论文标题
集团沉浸在独立二号的图表中，并具有某些禁忌子图
Clique immersions in graphs of independence number two with certain forbidden subgraphs
论文作者
论文摘要
Lescure-Meyniel猜想是Hadwiger猜想沉浸式命令的类似物。它指出，每个图$ g $都包含完整的图形$ k_ {χ（g）} $作为沉浸式，并且就像其次要订单对应物一样，即使对于具有独立数字2的图形也是开放的。我们证明，每个图$ g $ a Indeptirals $ lumber $α（g）\ ge 2 $ and ge 2 $ and No thength and Bone tength of 4 $ $ $ $ $ 2 $ $ 2 $ $ 2 $ $ $ 2 $ $满足。特别是，每个$ c_4 $ free Graph $ g $ at $α（g）= 2 $都满足Lescure-Meyniel的猜想。如下所示，我们给出了这种推论的另一个概括。令$ g $和$ h $是具有独立号码的图形，为$ | v（h）| \ le 4 $。如果$ g $是$ h $ free，则$ g $满足Lescure-Meyniel的猜想。
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 $K_{χ(G)}$ 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 $α(G)\ge 2$ and no hole of length between $4$ and $2α(G)$ satisfies this conjecture. In particular, every $C_4$-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 $|V(H)|\le 4$. If $G$ is $H$-free, then $G$ satisfies the Lescure-Meyniel conjecture.
