Geodesic
Planar graphs as minimal resolutions of trivariate monomial ideals
Documenta mathematica, Tome 7 (2002), pp. 43-90.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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) find 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.
Classification : 05C10, 13D02, 06A07, 13F55, 68R10, 52Cxx
Keywords: planar graph, monomial ideal, free resolution, order dimension, (rigid) geodesic embedding 
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     author = {Miller, Ezra},
     title = {Planar graphs as minimal resolutions of trivariate monomial ideals},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a17/}
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Miller, Ezra. Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta mathematica, Tome 7 (2002), pp. 43-90. http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a17/