3 problems

Let $W_n$ be a wheel graph and let $C(n,n)$ be the corresponding Ferris Wheel graph, for $n\geq 3$. Suppose Player X wins on $W_n$ with score $(a,b)$. Ferris Wheel score conjecture…

Let $C(n,k)$ be a loopy cycle formed from a cycle $C_n$ by adding $k$ loops to consecutive vertices, with $n\geq 3$. Loopy-cycle winner conjecture. For $k=1$ and $k=2$, Player 1 wi…

Let $G$ be a graph, and let $G'$ be obtained by adding a single loop to an existing vertex of $G$. Loop addition conjecture. Adding a single loop to an existing vertex always swaps…