bibkey: hartnellrallwash2017cartesian
authors: Bert L. Hartnell, Douglas F. Rall, Kirsti Wash
year: 2017
title: "On well-covered Cartesian products"
doi: null
url: https://arxiv.org/abs/1703.08716v1
claim: "Lemma 3.5 excludes well-covered Cartesian products of connected triangle-free factors of order at least three."
strata_touched:
  - D5/S3/Combinatorics/Graph/Products/CayleyCharacterization
license: citation-only
triage: anchor

Well-covered Cartesian products

Verified locator

https://arxiv.org/abs/1703.08716v1

Lemma 3.5, printed page 7, proves that the Cartesian product of connected graphs of order at least three and girth at least four is not well-covered. The introduction also recalls the well-coveredness of products of two complete graphs.

The Cayley square argument using a deleted-vertex coloring does not invoke Lemma 3.5. Its nearly empty layer treats connected graphs without a girth restriction. This note identifies the related published obstruction; it does not claim a Lean formalization of the general triangle-free product lemma.