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- W3046564315 abstract "Given two graphs $G$ and $G^*$ with a one-to-one correspondence between their edges, when do $G$ and $G^*$ form a pair of dual graphs realizing the vertices and countries of a map embedded in a surface? A criterion was obtained by Jack Edmonds in 1965. Furthermore, let $boldsymbol{d}=(d_1,ldots,d_n)$ and $boldsymbol{t}=(t_1,ldots,t_m)$ be their degree sequences. Then, clearly, $sum_{i=1}^n d_i = sum_{j=1}^m t_j = 2ell$, where $ell$ is the number of edges in each of the two graphs, and $chi = n - ell + m$ is the Euler characteristic of the surface. Which sequences $boldsymbol{d}$ and $boldsymbol{t}$ satisfying these conditions still cannot be realized as the degree sequences? We make use of Edmonds' criterion to obtain several infinite series of exceptions for the sphere, $chi = 2$, and projective plane, $chi = 1$. We conjecture that there exist no exceptions for $chi leq 0$." @default.
- W3046564315 created "2020-08-07" @default.
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- W3046564315 date "2020-08-02" @default.
- W3046564315 modified "2023-10-06" @default.
- W3046564315 title "On the degree sequences of dual graphs on surfaces." @default.
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