total dual integrality
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Author(s):  
Patrick Chervet ◽  
Roland Grappe ◽  
Louis-Hadrien Robert


2020 ◽  
Vol 34 (1) ◽  
pp. 470-496
Author(s):  
Marcel K. de Carli Silva ◽  
Levent Tunçel


2018 ◽  
Vol 274 (1-2) ◽  
pp. 531-553 ◽  
Author(s):  
Hanna Sumita ◽  
Naonori Kakimura ◽  
Kazuhisa Makino


Author(s):  
Xujin Chen ◽  
Zhuo Diao ◽  
Xiaodong Hu ◽  
Zhongzheng Tang


2012 ◽  
Vol 26 (3) ◽  
pp. 1022-1030 ◽  
Author(s):  
Xujin Chen ◽  
Zhibin Chen ◽  
Wenan Zang


2010 ◽  
Vol 132 (1-2) ◽  
pp. 57-78 ◽  
Author(s):  
Edwin O’Shea ◽  
András Sebö


10.37236/324 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
José Martínez-Bernal ◽  
Edwin O'Shea ◽  
Rafael H. Villarreal

If $\mathcal{C}$ is a clutter with $n$ vertices and $q$ edges whose clutter matrix has column vectors ${\mathcal A} = \{v_1, \ldots, v_q\}$, we call $\mathcal{C}$ an Ehrhart clutter if $\{(v_1,1),\ldots,(v_q,1)\} \subset \{ 0,1 \}^{n+1}$ is a Hilbert basis. Letting $A(P)$ be the Ehrhart ring of $P={\rm conv}(\mathcal{A})$, we are able to show that if $\mathcal{C}$ is a uniform unmixed MFMC clutter, then $\mathcal{C}$ is an Ehrhart clutter and in this case we provide sharp upper bounds on the Castelnuovo-Mumford regularity and the $a$-invariant of $A(P)$. Motivated by the Conforti-Cornuéjols conjecture on packing problems, we conjecture that if $\mathcal{C}$ is both ideal and the clique clutter of a perfect graph, then $\mathcal{C}$ has the MFMC property. We prove this conjecture for Meyniel graphs by showing that the clique clutters of Meyniel graphs are Ehrhart clutters. In much the same spirit, we provide a simple proof of our conjecture when $\mathcal{C}$ is a uniform clique clutter of a perfect graph. We close with a generalization of Ehrhart clutters as it relates to total dual integrality.



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