Spanning bipartite quadrangulations in even triangulations of real projective spaces
Abstract
We study spanning quadrangulations of even triangulations of real projective spaces, using the higher-dimensional notion of quadrangulation introduced by Kaiser and Stehl\'ık. We prove that every even triangulation of RPd, where d≥ 2, admits a spanning bipartite quadrangulation. Moreover, such a triangulation admits a spanning non-bipartite quadrangulation if and only if it is not balanced; if it is balanced, every spanning quadrangulation is bipartite. Our proofs use coloring monodromy: its orbits yield bipartite quadrangulations, while a covering-space construction gives non-bipartite ones. %In dimension three, a bipartite quadrangulation can always be chosen to induce K2,2 on each tetrahedron. More generally, we establish a sufficient condition for the existence of spanning bipartite quadrangulations on closed manifolds in terms of the monodromy action, and derive a consequence involving the fundamental group.
Related
- Geometric Realizations with Strong Self-Duality Part I: Non-Bipartite Quadrangulations of the Projective Plane and Strongly Involutive Self-Dual Graphs
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- Maximum number of spanning trees in bipartite graphs with a given diameter
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- Characterizing multigraded regularity and virtual resolutions on products of projective spaces
BibTeX
@misc{enami2026spanning,
title = {{Spanning bipartite quadrangulations in even triangulations of real projective spaces}},
author = {Kengo Enami},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29737},
eprint = {2610.29737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29737},
}
RIS
TY - UNPB
TI - Spanning bipartite quadrangulations in even triangulations of real projective spaces
AU - Kengo Enami
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29737
UR - https://arxiv.org/abs/2610.29737
AB - We study spanning quadrangulations of even triangulations of real projective spaces, using the higher-dimensional notion of quadrangulation introduced by Kaiser and Stehl\'ık. We prove that every even triangulation of RP^d, where d≥ 2, admits a spanning bipartite quadrangulation. Moreover, such a triangulation admits a spanning non-bipartite quadrangulation if and only if it is not balanced; if it is balanced, every spanning quadrangulation is bipartite. Our proofs use coloring monodromy: its orbits yield bipartite quadrangulations, while a covering-space construction gives non-bipartite ones. %In dimension three, a bipartite quadrangulation can always be chosen to induce K_2,2 on each tetrahedron. More generally, we establish a sufficient condition for the existence of spanning bipartite quadrangulations on closed manifolds in terms of the monodromy action, and derive a consequence involving the fundamental group.
ER -