4 problems

Erdős–Füredi–Gould–Gunderson conjecture. The same formula should hold for all $1\leq k\leq n/4$. Their conjecture extends the known range of the exact Turán-number formula for fans…

Let $P_n$ be the path graph on $n\geq 1$ vertices, let $K_1$ be the singleton graph, and let $K_1+P_n$ denote their graph join. Write $\mathrm{QEC}(K_1+P_n)$ for the quadratic embe…

Let $V_{k+1}=K_1\vee P_k$ be the fan graph on $k+1$ vertices, and let $G$ be a graph with $m$ edges and spectral radius $\rho(G)$. Li–Lu–Peng fan-graph conjecture. For…

Fan-free spectral extremal conjecture. If $G$ is a $V_{2k+1}$-free or $V_{2k+2}$-free graph with $m$ edges, then