A.M.H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica 6 (4), (1986), 365-379. Home/Search Document Not in Database Summary Related Articles Check |
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The Stable Set Problem and the Lift-and-Project Ranks of Graphs - Liptak, Tuncel (2002) (Correct)
....(b) is not satis ed, then four vertices of K n induce the graph shown on Figure 3 in G (or a graph having an odd number of vertices on the paths 1 2, 2 4, 4 3, and 3 1) Thus, deleting the remaining n 4 vertices of K n leaves this graph plus possibly paths. It was shown by Gerards and Schrijver [8] that the N 0 rank of such a graph is 1, thus again G has N 0 rank at most n 3. When G is an odd star subdivision of K n , we have already seen that its N 0 and N rank are both n 2, and the theorem is proved. Lov asz and Schrijver [16] proved r(K n ) n 2 by showing that the point x = ....
A. M. H. Gerards and A. Schrijver, Matrices with the Edmonds{Johnson property, Combinatorica 6 (1986) 365-379.
A Combinatorial Algorithm for Computing a Maximum.. - Eisenbrand, Funke.. (2002) (2 citations) (Correct)
....of t perfect graphs, which are those graphs G, for which P odd (G) is a 0 1 polytope. The odd cycle inequalities can be separated in polynomial time, i.e. one can decide in polynomial time whether one of the inequalities (1. 2) violates a given point x and if so, compute such an inequality [6]. It follows thus that the ellipsoid method can be used to optimize a linear function over P odd (G) in polynomial time and consequently solve the weighted stable set problem for t perfect graphs in polynomial time. The ellipsoidal algorithm is heavily based on division, rounding and ....
....graphs has, so far, not been provided. However some subclasses of t perfect graphs have been identified which can be characterized and recognized in polynomial time. These include bipartite graphs, almost bipartite graphs [4] series parallel graphs [1, 2] graphs that do not contain an odd K 4 [6] and graphs that do not contain a so called bad K 4 [7] Combinatorial algorithms for the stable set problem have been provided for bipartite graphs, almost bipartite graphs [4] and series parallel graphs [1, 2] The search for combinatorial algorithms for polynomial problems for which only ....
A. M. H. Gerards and A. Schrijver. Matrices with the Edmonds-Johnson property. Combinatorica, 6:365-- 379, 1986.
On the Separation of Split Cuts and Related Inequalities - Caprara, Letchford (1 citation) (Correct)
....to show how to minimize any linear function over the associated P I (or prove unboundedness) in polynomial time. If the optimal value is indeed bounded, then the minimization problem amounts to nding a minimum weight odd circuit in G. This can be done using the algorithm of Gerards Schrijver [14]. Therefore, all of the above mentioned separation problems remain strongly NP complete even when P has only one vertex, and even when optimization over P I is polynomial time solvable. 3.3 Separation when the disjunction is xed The results of the previous subsection paint a rather bleak ....
A.M.H. Gerards & A. Schrijver, Matrices with the Edmonds-Johnson property". Combinatorica, vol. 6, pp. 365-379, 1986.
Applying Lehman's Theorems to Packing Problems - Shepherd (1995) (2 citations) (Correct)
.... x v 1; uv 2 EG ) and the odd cycle inequalities (x(V (C) ff jCj ; for each odd cycle C of G) The following is immediate from Theorem 19. Corollary 23 A near bipartite graph G is t perfect if and only if it has no odd wheels and no prime antiwebs other than odd holes. Gerards and Schrijver [11] showed that a graph with no subgraph which is an odd K 4 is t perfect. An odd K 4 is any graph obtained by subdividing the edges of a K 4 in such a way, that the images of the four triangles become odd cycles. Note that the class of t perfect graphs given by Corollary 23 is not contained in ....
A.M.H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica 6 (4), (1986), 365-379.
Algorithms Based on LP Relaxations for Combinatorial Optimization .. - Caprara (Correct)
....[51] and Nemhauser and Wolsey [45] Examples of EPT matrices include the f0; 1g matrices having no more than two 1 s per column, and those in which the 1 s in a column occur consecutively. Theorem 4 f0; 1 2 g SEP can be solved in polynomial time if A T is an EPT matrix. Gerards and Schrijver [35] gave a polynomial time algorithm for f0; 1 2 g SEP when A is an integer matrix satisfying P j ja ij j 2 for each row index i. More generally, Theorem 4 implies that f0; 1 2 g SEP can be solved efficiently when A has, at most, two odd coefficients in each row. Theorem 5 f0; 1 2 g SEP can ....
A.M.H. Gerards and A. Schrijver, "Matrices with the Edmonds-Johnson Property", Combinatorica 6 (1986) 365--379.
Strong t-perfection of bad-K4-free graphs - Schrijver Self-citation (Schrijver) (Correct)
....an odd K 4 , if each triangle of K 4 has become an odd circuit in H . It was shown by Gerards [7] that each graph without odd K 4 is strongly t perfect. 3) By a graph without odd K 4 we mean a graph not containing an odd K 4 as subgraph. It extends an earlier result of Gerards and Schrijver [8] that such graphs are t perfect. There exist however odd K 4 s that are t perfect. Following Gerards and Shepherd [9] we call an odd K 4 subdivision a bad K 4 if it does not have the following property: the edges of K 4 that have become an even path, form a 4 cycle in K 4 , while the two other ....
A.M.H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica 6 (1986) 365-379.
Strong t-perfection of bad-K_4-free graphs - Schrijver Self-citation (Schrijver) (Correct)
....an odd K 4 , if each triangle of K 4 has become an odd circuit in H. It was shown by Gerards [7] that each graph without odd K 4 is strongly t perfect. 3) By a graph without odd K 4 we mean a graph not containing an odd K 4 as subgraph. It extends an earlier result of Gerards and Schrijver [8] that such graphs are t perfect. There exist however odd K 4 s that are t perfect. Following Gerards and Shepherd [9] we call an odd K 4 subdivision a bad K 4 if it does not have the following property: the edges of K 4 that have become an even path, form a 4 cycle in K 4 , while the two other ....
A.M.H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica 6 (1986) 365--379.
Applying Lehman's Theorems to Packing Problems - Shepherd (1995) (2 citations) (Correct)
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A.M.H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica 6 (4), (1986), 365-379.
A Bidirected Generalisation of Network Matrices - Appa, Kotnyek (2002) (Correct)
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A.M.H. Gerards and A. Schrijver. Matrices with the Edmonds-Johnson property. Combinatorica, 6:365-- 379, 1986.
A Generalization of Totally Unimodular and Network Matrices - Kotnyek (2002) (Correct)
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A.M.H. Gerards and A. Schrijver. Matrices with the Edmonds-Johnson property. Combinatorica, 6:365--379, 1986.
A Generalization of Totally Unimodular and Network Matrices - Kotnyek (2002) (Correct)
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A.M.H. Gerards and A. Schrijver. Matrices with the Edmonds-Johnson property. Combinatorica, 6:365--379, 1986.
A Generalization of Totally Unimodular and Network Matrices - Kotnyek (2002) (Correct)
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A.M.H. Gerards and A. Schrijver. Matrices with the Edmonds-Johnson property. Combinatorica, 6:365--379, 1986.
Packing a Trunk - Eisenbrand, Funke, Reichel, Schömer (Correct)
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Gerards, A.M.H., Schrijver, A.: Matrices with the Edmonds-Johnson property. Combinatorica 6 (1986) 365--379
Integer Polyhedra: Combinatorial Properties and Complexity - Sebö (2001) (Correct)
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A. M. H. Gerards, A. Schrijver, Matrices with the Edmonds-Johnson property, Combinatorica, 6 (1986), 365-379.
Primal Separation Algorithms - Letchford, Lodi (2001) (Correct)
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A.M.H. Gerards & A. Schrijver (1986) Matrices with the Edmonds-Johnson property. Combinatorica 6, 365--379.
Polyhedral Techniques in Combinatorial Optimization I: Theory - Aardal, van Hoesel (1995) (1 citation) (Correct)
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A.M.H. Gerards and A. Schrijver (1986) "Matrices with the Edmonds-Johnson property ", Combinatorica 6 365--389.
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