Hernán de Alba, Walter Carballosa, Daniel Duarte, Luis Manuel Rivera: Cohen-Macaulayness of triangular graphs p. 103-112

Abstract:

We study the Cohen-Macaulay property of triangular graphs $T_n$. We show that $T_2$, $T_3$ and $T_5$ are Cohen-Macaulay graphs, and that $T_4$, $T_6$, $T_8$ and $T_n$ are not Cohen-Macaulay graphs, for $n \geq 10$. Finally, we prove that over fields of characteristic zero $T_7$ and $T_9$ are Cohen-Macaulay.

Key Words: Triangular graphs, edge ideals, Cohen-Macaulay graphs

2010 Mathematics Subject Classification: Primary 13F55,
Secondary 13H10, 05C75.

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