PreprintCC BY 4.0HAL
Power-of-two cycles in projective cubic graphs of large edge-width
Abstract
Heckman and Krakovski proved that every 3-connected cubic planar graph contains a cycle of length 2^m for some 2 ≤ m ≤ 7. We extend this to 3-connected cubic graphs embedded in the real projective plane with face-width at least three and edge-width at least 48; the cycle may moreover be taken contractible. The argument passes to the spherical double cover, where the planar theorem provides the cycle inside a subgraph of diameter at most 47, and the condition on the edge-width guarantees that this subgraph projects injectively.
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BibTeX
@misc{culus2026poweroftwo,
title = {{Power-of-two cycles in projective cubic graphs of large edge-width}},
author = {Jean-François Culus},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26403},
eprint = {2610.26403},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05803055v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Power-of-two cycles in projective cubic graphs of large edge-width
AU - Jean-François Culus
PY - 2026
DA - 2026/10/15
PB - HAL
DO - 10.48550/arxiv.2610.26403
UR - https://hal.science/hal-05803055v1
AB - Heckman and Krakovski proved that every 3-connected cubic planar graph contains a cycle of length 2^m for some 2 ≤ m ≤ 7. We extend this to 3-connected cubic graphs embedded in the real projective plane with face-width at least three and edge-width at least 48; the cycle may moreover be taken contractible. The argument passes to the spherical double cover, where the planar theorem provides the cycle inside a subgraph of diameter at most 47, and the condition on the edge-width guarantees that this subgraph projects injectively.
ER -