Planar graphs as minimal resolutions of trivariate monomial ideals
By Ezra Miller. Documenta Mathematica, 2002
57 citations recorded by the source corpus.
We introduce the notion of rigid embedding in a grid surface, a new kind of plane drawing for simple triconnected planar graphs. Rigid embeddings provide methods to (1) flnd well-structured (cellular, here) minimal free resolutions for arbitrary monomial ideals in three variables; (2) strengthen the Brightwell{Trotter bound on the order dimension of triconnected planar maps by giving a geometric reformulation; and (3) generalize Schnyder's angle coloring of planar triangulations to arbitrary triconnected planar maps via geometry. The notion of rigid embedding is stable under duality for planar maps, and has certain uniqueness properties.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/d1ce27081e214732dbb7ff71ebf6241ccd2e270b
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Geometric Graphs and Arrangements (2004, background): “For valuable discussions and for help by way of comments and corrections I want to thank Patrick Baier, Peter Braß, Frank Hoffmann, Klaus Kriegel, Mareike Massow, Ezra Miller, Walter Morris, János Pach, Günter Rote, Sarah Renkl, Volker Schulz, Ileana Streinu, Tom Trotter, Pavel Valtr, Uli Wagner, ”