The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1051 |
| Date | 01 May 2013 |
| Creators | Gaslowitz, Joshua Z |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
| Rights | J. Zachary Gaslowitz |
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