10 citations · 10 across the 3 of their papers we have counts for
5 papers
An Randomized Lower Bound for Cutting a Cake into Proportionally Fair Pieces
Stephen Arndt, Kirk Pruhs, Trung Tran
We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use …
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 .
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…
Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals
Le Tuan Hoa, Tran Nam Trung
Let be a monomial ideal in a polynomial ring . In this paper we give an upper bound on $\overline{\dstab} (I)$ in terms of and the maximal generatin…
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.