Some results on an algebro-geometric condition on graphs
Combinatorics
2017-01-11 v3 Algebraic Geometry
Abstract
Paolo Aluffi, inspired by an algebro-geometric problem, asked when the Kirchhoff polynomial of a graph is in the Jacobian ideal of the Kirchhoff polynomial of the same graph with one edge deleted. We give some results on which graph-edge pairs have this property. In particular we show that multiple edges can be reduced to double edges, we characterize which edges of wheel graphs satisfy the property, we consider a stronger condition which guarantees the property for any parallel join, and we find a class of series-parallel graphs with the property.
Keywords
Cite
@article{arxiv.1602.00356,
title = {Some results on an algebro-geometric condition on graphs},
author = {Avi Kulkarni and Gregory Maxedon and Karen Yeats},
journal= {arXiv preprint arXiv:1602.00356},
year = {2017}
}
Comments
36 pages. Typo correction as suggested by referee