A coloring property for stable allocations

• The anti-blocking property for stable allocations and stable flows is proved.
• This is an improvement of previously known results for stable bb-matchings.
• The results are also extended to stable flows and allocations with choice functions.

We prove that in the stable allocations problem for a fixed vertex vv there can be done a partition of the edges incident with vv such that in any stable allocation there is at most one edge incident with vv from each class. This is an improvement of the coloring theorem for stable bb-matchings given in Fleiner (2003). We also extend our result to stable flows and allocations with choice functions.