# An upper bound for the regularity of binomial edge ideals of trees

TL;DR: In this article, an improved upper bound for the regularity of binomial edge ideals of trees was obtained, which was later extended to the case of trees with binomial edges.

Abstract: In this article, we obtain an improved upper bound for the regularity of binomial edge ideals of trees.

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##### Citations

17 citations

### Cites methods from "An upper bound for the regularity o..."

...Also using the upper bound proved in [10], we get reg S/JG ≤ 6....

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### Cites background from "An upper bound for the regularity o..."

...This bound, in general, is a weak one and there are improved bounds for several classes, (see for example [14, 21, 25, 29, 30, 31, 40])....

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### Cites background from "An upper bound for the regularity o..."

...obtained improved bounds for the regularity of binomial edge ideals of trees, [7, 8]....

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##### References

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### Additional excerpts

..., [4] and independently by Ohtani [11]....

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### Additional excerpts

..., [4] and independently by Ohtani [11]....

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...This notion was introduced by Herzog et al., [4] and independently by Ohtani [11]....

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### "An upper bound for the regularity o..." refers background in this paper

...rity of the binomial edge ideals using combinatorial invariants. It is known that ℓ≤ reg(S/J G) ≤ n− 1, where n is the number of vertices in G and ℓ denotes the length of a longest induced path in G, [10]. Further, in the same article, Matsuda and Murai conjectured that reg(S/J G) = n− 1 if and only if Gis a path. This conjecture was settled in the aﬃrmative by Kiani and Saeedi Madani, [8]. A vertex v...

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