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Intro; Preface; Acknowledgements; Contents; About the Editors; 1 A Unified Framework for a Class of Mathematical Programming Problems; 1.1 Introduction; 1.2 Preliminaries; 1.3 A Class of Mathematical Programming Problems in Complementarity Framework; 1.3.1 Linear Programming; 1.3.2 Quadratic Programming; 1.3.3 Linear Fractional Programming Problem; 1.3.4 Nash Equilibrium and Bimatrix Games; 1.3.5 Computational Complexity of LCP; 1.4 Matrix Classes in LCP; 1.5 Lemke's Algorithm; 1.6 Some Recent Matrix Classes and Lemke's Algorithm; 1.6.1 Positive Subdefinite Matrices
1.6.2 barN (Almost barN-Matrix)1.6.3 Fully Cospositive Matrices; 1.7 Hidden Z-Matrices; 1.8 Various Generalizations of LCP; 1.8.1 Vertical Linear Complementarity Problem; 1.8.2 Scarf's Complementarity Problem; 1.8.3 Other Generalizations; References; 2 Maximizing Spectral Radius and Number of Spanning Trees in Bipartite Graphs; 2.1 Introduction; 2.2 Ferrers Graphs; 2.3 Maximizing the Spectral Radius of a Bipartite Graph; 2.4 The Number of Spanning Trees in a Ferrers Graph; 2.5 Maximizing the Number of Spanning Trees in a Bipartite Graph; 2.6 A Reformulation in Terms of Majorization
2.7 Resistance Distance in G and G {f}2.8 The Number of Spanning Trees in Ferrers Graphs; References; 3 Optimization Problems on Acyclic Orientations of Graphs, Shellability of Simplicial Complexes, and Acyclic Partitions; 3.1 An Optimization Problem on Acyclic Orientation of Graphs in the Theory of Polytopes; 3.2 Shellability of Simplicial Complexes and Orientations of Facet-Ridge Incidence Graphs; 3.2.1 The Case of Pure Simplicial Complexes; 3.2.2 The Case of Nonpure Simplicial Complexes; 3.3 Cubical Complexes and Acyclic Partitions
3.4 Optimization of Orientation of Graphs Without Acyclicity ConstraintReferences; 4 On Ideal Minimally Non-packing Clutters; 4.1 Introduction; 4.1.1 Background and Motivation; 4.1.2 Overview of Our Results; 4.2 Preliminaries; 4.3 Precore Conditions; 4.3.1 Integral Blocking Condition; 4.3.2 Tilde-Invariant Clutters and Tilde-Full Condition; 4.3.3 Polytope I(calC); 4.3.4 Non-separability; 4.3.5 Summarizing the Conditions in Step 1; 4.4 Conditions in the Second Step; 4.5 Unique Maximum Fractional Packing; 4.5.1 Unique Maximum Fractional Packing; 4.5.2 Combinatorial Affine Planes; References
5 Symmetric Travelling Salesman Problem5.1 Introduction; 5.2 Preliminaries; 5.2.1 Graph Theory; 5.3 Formulations for the TSP; 5.3.1 Dantzig, Fulkerson and Johnson; 5.3.2 Cycle Shrink; 5.3.3 The Multistage Insertion Formulation for the STSP; 5.3.4 The Pedigree Polytope; 5.3.5 Comparisons; 5.4 Hypergraphs; 5.5 Hypergraph Simplex; 5.6 MI formulation in Hypergraph; 5.7 Implementation of Hypergraph Approach; 5.8 Concluding Remarks; References; 6 About the Links Between Equilibrium Problems and Variational Inequalities; 6.1 Introduction and Motivation; 6.2 State of the Art of Relationships
1.6.2 barN (Almost barN-Matrix)1.6.3 Fully Cospositive Matrices; 1.7 Hidden Z-Matrices; 1.8 Various Generalizations of LCP; 1.8.1 Vertical Linear Complementarity Problem; 1.8.2 Scarf's Complementarity Problem; 1.8.3 Other Generalizations; References; 2 Maximizing Spectral Radius and Number of Spanning Trees in Bipartite Graphs; 2.1 Introduction; 2.2 Ferrers Graphs; 2.3 Maximizing the Spectral Radius of a Bipartite Graph; 2.4 The Number of Spanning Trees in a Ferrers Graph; 2.5 Maximizing the Number of Spanning Trees in a Bipartite Graph; 2.6 A Reformulation in Terms of Majorization
2.7 Resistance Distance in G and G {f}2.8 The Number of Spanning Trees in Ferrers Graphs; References; 3 Optimization Problems on Acyclic Orientations of Graphs, Shellability of Simplicial Complexes, and Acyclic Partitions; 3.1 An Optimization Problem on Acyclic Orientation of Graphs in the Theory of Polytopes; 3.2 Shellability of Simplicial Complexes and Orientations of Facet-Ridge Incidence Graphs; 3.2.1 The Case of Pure Simplicial Complexes; 3.2.2 The Case of Nonpure Simplicial Complexes; 3.3 Cubical Complexes and Acyclic Partitions
3.4 Optimization of Orientation of Graphs Without Acyclicity ConstraintReferences; 4 On Ideal Minimally Non-packing Clutters; 4.1 Introduction; 4.1.1 Background and Motivation; 4.1.2 Overview of Our Results; 4.2 Preliminaries; 4.3 Precore Conditions; 4.3.1 Integral Blocking Condition; 4.3.2 Tilde-Invariant Clutters and Tilde-Full Condition; 4.3.3 Polytope I(calC); 4.3.4 Non-separability; 4.3.5 Summarizing the Conditions in Step 1; 4.4 Conditions in the Second Step; 4.5 Unique Maximum Fractional Packing; 4.5.1 Unique Maximum Fractional Packing; 4.5.2 Combinatorial Affine Planes; References
5 Symmetric Travelling Salesman Problem5.1 Introduction; 5.2 Preliminaries; 5.2.1 Graph Theory; 5.3 Formulations for the TSP; 5.3.1 Dantzig, Fulkerson and Johnson; 5.3.2 Cycle Shrink; 5.3.3 The Multistage Insertion Formulation for the STSP; 5.3.4 The Pedigree Polytope; 5.3.5 Comparisons; 5.4 Hypergraphs; 5.5 Hypergraph Simplex; 5.6 MI formulation in Hypergraph; 5.7 Implementation of Hypergraph Approach; 5.8 Concluding Remarks; References; 6 About the Links Between Equilibrium Problems and Variational Inequalities; 6.1 Introduction and Motivation; 6.2 State of the Art of Relationships