PreprintCC BY 4.0arXiv
Monophobic Neighborhoods of Cubes
Abstract
We define a d-cube in a graph G to be monophobic in G if, whenever it supports a d-face of a discrete singular d+1-cube, it must also support another face. In many cases, the presence of such cubes implies the nontriviality of discrete cubical homology and homotopy groups associated with G. We describe several large classes of examples and characterize the property completely when d=2.
Related
BibTeX
@misc{greene2026monophobic,
title = {{Monophobic Neighborhoods of Cubes}},
author = {Curtis Greene and Samira Sahar Jamil},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14502},
eprint = {2610.14502},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14502},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monophobic Neighborhoods of Cubes
AU - Curtis Greene
AU - Samira Sahar Jamil
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14502
UR - https://arxiv.org/abs/2610.14502
AB - We define a d-cube in a graph G to be monophobic in G if, whenever it supports a d-face of a discrete singular d+1-cube, it must also support another face. In many cases, the presence of such cubes implies the nontriviality of discrete cubical homology and homotopy groups associated with G. We describe several large classes of examples and characterize the property completely when d=2.
ER -