Pith. sign in

REVIEW 1 cited by

Diameter and spectral gap for planar graphs

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1204.4435 v2 pith:T7HKMPLL submitted 2012-04-19 math.GT math.PR

Diameter and spectral gap for planar graphs

classification math.GT math.PR
keywords graphsplanardiamspectralaboveanswerbenjaminibounded
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
abstract

We prove that the spectral gap of a finite planar graph $X$ is bounded by $\lambda_1(X)\le C(\frac{\log(\diam X)}{\diam X})^2$ where $C$ depends only on the degree of $X$. We then give a sequence of such graphs showing the the above estimate cannot be improved. This yields a negative answer to a question of Benjamini and Curien on the mixing times of the simple random walk on planar graphs.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks

    cs.LG 2025-08 conditional novelty 6.0

    A learned triangle-selection module rewires graphs for GNNs, improving node classification over prior rewiring methods on 9 of 10 benchmarks.