占有数に上限のあるトークングラフのマッチングと独立数

A token configuration assigns nonnegative occupancies of total size k to the vertices of a graph; a move transfers one token along one edge. We prove the independence-number conjecture of Reyes, Dalfó and Fiol for these graphs with unrestricted occupancy. If a bipartite base graph has a matching saturating one part, its token graph has a matching saturating every configuration with odd occupancy on that part. The even configurations therefore form a maximum independent set. The same conclusion holds for every even finite occupancy bound. A decomposition into products of paths gives sharp matching and independence bounds for arbitrary hosts and a sufficient condition for unequal vertex capacities, with a complete classification of the relevant two-vertex condition. For every odd finite capacity we exhibit a bipartite host whose token graph has an independent set larger than both parity classes. We also obtain exact Shannon capacities in the saturated cases and asymptotic matching densities as the number of tokens grows.