Abstract
AbstractTropical curves in $${\mathbb {R}}^2$$
R
2
correspond to metric planar graphs but not all planar graphs arise in this way. We describe several new classes of graphs which cannot occur. For instance, this yields a full combinatorial characterization of the tropically planar graphs of genus at most five.
Funder
Technische Universität Berlin
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Reference13 articles.
1. Balaban, A.T.: Chemical Applications of Graph Theory. Academic Press, New York (1976)
2. Brodsky, S., Joswig, M., Morrison, R., Sturmfels, B.: Moduli of tropical plane curves. Res. Math. Sci. (2015). https://doi.org/10.1186/s40687-014-0018-1
3. Cartwright, D., Dudzik, A., Manjunath, M., Yao, Y.: Embeddings and immersions of tropical curves. Collect. Math. 67(1), 1–19 (2016). https://doi.org/10.1007/s13348-015-0149-8
4. Castryck, W., Voight, J.: On nondegeneracy of curves. Algebra Numb. Theory 3(3), 255–281 (2009)
5. Coles, D., Dutta, N., Jiang, S., Morrison, R., Scharf, A.: Tropically planar graphs (2019). Preprint arXiv:1908.04320v3
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Generalised cone complexes and tropical moduli in polymake;Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation;2023-07-24
2. Characterization of tropical plane curves up to genus six;Archiv der Mathematik;2023-02-22
3. Smooth tropical complete intersection curves of genus 3 in $$\mathbb {R}^3$$;Collectanea Mathematica;2022-08-27
4. Tropically planar graphs;Collectanea Mathematica;2021-10-07
5. Prism graphs in tropical plane curves;Involve, a Journal of Mathematics;2021-07-17