3 problems

Let $G$ be a graph, and let $D$ and $W$ be distributions on $G$. A value function is any function $A$ on the set of distributions satisfying the two properties of the standard valu…

Let $G=(V,E)$ be a graph. A distribution of pebbles on $G$ is an initial arrangement of pebbles on a subset of vertices, and its support is that subset. Let $\gamma(G)$ denote the…

Let $G$ and $H$ be graphs. A nonnegative function on a graph assigns a nonnegative real number to each vertex. Let $\omega_1$ be a nonnegative function on $G$ and $\omega_2$ a nonn…