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arXiv · 1708.08864

On $m$-Closed Graphs

Leila Sharifan·Masoumeh Javanbakht
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Abstract

A graph is closed when its vertices have a labeling by $[n]$ such that the binomial edge ideal $J_G$ has a quadratic Gr\"{o}bner basis with respect to the lexicographic order induced by $x_1 > \cdots > x_n > y_1> \cdots > y_n$. In this paper, we generalize this notion and study the so called $m-$closed graphs. We find equivalent condition to $3-$closed property of an arbitrary tree $T$. Using it, we classify a class of $3-$closed trees. The primary decomposition of this class of graphs is also studied.

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Leila Sharifan, Masoumeh Javanbakht. 2017-08-29. On $m$-Closed Graphs. https://arxiv.org/abs/1708.08864

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