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Brill-Noether Conjecture on Cactus Graphs

Abstract

We give a proof of the combinatorial Brill-Noether conjecture for cactus graphs. This conjecture was formulated by Baker in 2008 when studying the interaction between algebraic curves theory and graph theory. By analyzing the treelike structure of cactus graphs, we produce a construction proof that is based on the Chip Firing Game theory.

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Funding

This work was partially supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the grant number 101.99-2016.16 and by the Vietnam Institute for Advanced Study in Mathematics (VIASM).

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Correspondence to Phan Thi Ha Duong.

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Duong, P.T.H. Brill-Noether Conjecture on Cactus Graphs. Acta Math Vietnam (2022). https://doi.org/10.1007/s40306-021-00475-6

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  • DOI: https://doi.org/10.1007/s40306-021-00475-6

Keywords

  • Brill-Noether conjecture
  • Cactus graph
  • Chip firing game
  • Cycle
  • Rank of divisors on graphs

Mathematics Subject Classification (2010)

  • 05C38
  • 68R10