Chip-firing based methods in the Riemann-Roch theory of directed graphs

Bálint Hujter, Lilla Tóthmérész


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}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2016},
NUMBER = {TR-2016-01}

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