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math.AC2023
Cohen-Macaulay oriented graphs with large girth
Le Xuan Dung, Tran Nam Trung
We classify the Cohen-Macaulay weighted oriented graphs whose underlying graphs have girth at least .
math.AC2018
Regularity, matchings and Cameron-Walker graphs
Tran Nam Trung
Let be a simple graph and let be the matching number of . It is well-known that $\reg I(G) \leqslant ν(G)+1$. In this paper we show that $\reg I(G) = ν(G)+1$ if and o…
math.AC2016
A Characterization of Gorenstein Planar graphs
Tran Nam Trung
We prove that a planar graph is Gorenstein if and only if its independence complex is Eulerian.