On the 0, 1 facets of the set covering polytope
Mathematical Programming: Series A and B
Lehman's forbidden minor characterization of ideal 0–1 matrices
Discrete Mathematics
Mathematical Programming: Series A and B
Applying Lehman's theorems to packing problems
Mathematical Programming: Series A and B
Journal of Combinatorial Theory Series B
The disjunctive procedure and blocker duality
Discrete Applied Mathematics
A Generalization of the Perfect Graph Theorem Under the Disjunctive Index
Mathematics of Operations Research
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
The nonidealness index of rank-ideal matrices
Discrete Applied Mathematics
On packing and covering polyhedra of consecutive ones circulant clutters
Discrete Applied Mathematics
On the set covering polyhedron of circulant matrices
Discrete Optimization
| Hi-index | 0.00 |
In this paper we define the class of near-ideal clutters following a similar concept due to Shepherd [Near perfect matrices, Math. Programming 64 (1994) 295-323] for near-perfect graphs. We prove that near-ideal clutters give a polyhedral characterization for minimally nonideal clutters as near-perfect graphs did for minimally imperfect graphs. We characterize near-ideal blockers of graphs as blockers of near-bipartite graphs. We find necessary conditions for a clutter to be near-ideal and sufficient conditions for the clutters satisfying that every minimal vertex cover is minimum.