4 problems

Let $P_k$ be the path on $k$ vertices, and let $\widehat P_k$ be the graph obtained from $P_k$ by adding a new vertex adjacent to every vertex of $P_k$. For a graph $G$, write…

For a graph $G$, let $t(G)$ denote its number of triangles. Let $W_k$ be the wheel formed by joining a new vertex to every vertex of a $k$-cycle, and let $W_{\ge 3}$ denote the fam…

Triangle-count conjecture. If

Let $G$ be an $n$-vertex graph, let $T(G)$ denote its number of triangles, and let $\tau_{\triangle}(G)$ be the minimum size of a vertex set meeting every triangle. For integers…