3 problems

Let $G$ be a graph on $n$ vertices, and let $\mathrm{bk}(G)$ denote the largest integer $r$ such that $G$ contains $r$ triangles sharing a common edge. Erdős's booksize conjecture.…

Let $G$ be a non-bipartite graph with $m$ edges, and let $B_{r+1}$ denote the graph formed by $r+1$ triangles sharing a common edge. Let $S^+_{m,1}$ be the graph obtained by adding…

Booksize lower-bound conjecture. If