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Baker and Norine proved a Riemann-Roch theorem for divisors on undirected graphs.
The notions of graph divisor theory are in duality with the notions of the chip-firing game.
Based on this connection, we give a new proof for the Riemann-Roch theorem on graphs which
can be generalized to Eulerian directed graphs, improving a result of Amini and Manjunath.
We also give a graph-theoretic version of the abstract Riemann-Roch criterion of Baker and Norine,
and explore the natural Riemann-Roch property introduced by Asadi and Backman.
Previous version can be found here.
Bibtex entry:
| AUTHOR | = | {Hujter, B{\'a}lint and T{\'o}thm{\'e}r{\'e}sz, Lilla}, |
| TITLE | = | {Chip-firing based methods in the Riemann-Roch theory of directed graphs}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2016}, |
| NUMBER | = | {TR-2016-01} |