PreprintCC BY 4.0arXiv
Almost Gorenstein edge rings of bipartite graphs and their h-vectors
Abstract
We characterize bipartite graphs whose edge rings are almost Gorenstein. Using this characterization, we recover known results for two families of graphs. In addition, we show that if the edge ring of a bipartite graph is almost Gorenstein and its h-polynomial has degree at least two, then the h-polynomial is palindromic except possibly for the linear and next-to-leading coefficients. Moreover, we construct two bipartite graphs whose edge rings have the same h-vector, although only one of the rings is almost Gorenstein.
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BibTeX
@misc{hatasa2026almost,
title = {{Almost Gorenstein edge rings of bipartite graphs and their $h$-vectors}},
author = {Yuta Hatasa and Koji Matsushita},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01032},
eprint = {2611.01032},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01032},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Almost Gorenstein edge rings of bipartite graphs and their h-vectors
AU - Yuta Hatasa
AU - Koji Matsushita
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01032
UR - https://arxiv.org/abs/2611.01032
AB - We characterize bipartite graphs whose edge rings are almost Gorenstein. Using this characterization, we recover known results for two families of graphs. In addition, we show that if the edge ring of a bipartite graph is almost Gorenstein and its h-polynomial has degree at least two, then the h-polynomial is palindromic except possibly for the linear and next-to-leading coefficients. Moreover, we construct two bipartite graphs whose edge rings have the same h-vector, although only one of the rings is almost Gorenstein.
ER -