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An LLM-Enhanced Adversarial Editing System for Lexical Simplification
Lexical Simplification (LS) aims to simplify text at the lexical level.
Spectral extrema of graphs with fixed size: cycles and complete bipartite graphs
We first show that if $\rho(G)\geq \sqrt{m}$, then $G$ contains $K_{2, r+1}$ unless $G$ is a star; and $G$ contains either $C_3^+$ or $C_4^+$ unless $G$ is a complete bipartite graph, where $C_t^+$ denotes the graph obtained from $C_t$ and $C_3$ by identifying an edge.
Combinatorics 05C50
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