| Preface | |
| Basic Terminology | |
| Threshold Graphs | |
| Motivation | |
| Basic characterizations | |
| Minimizing integral weights | |
| Perfect graphs and algorithms | |
| Threshold and split completions | |
| Longest cycles and Hamiltonicity | |
| Total coverings and total matchings | |
| Ferrers Digraphs and Difference Graphs | |
| Introduction | |
| Ferrers digraphs, characterizations | |
| The Ferrers dimension | |
| Difference graphs | |
| Degree Sequences | |
| Graphical degree sequences | |
| Threshold sequences | |
| The polytope of degree sequences | |
| Difference sequences | |
| Applications.Introduction | |
| Aggregation of inequalities | |
| Synchronization | |
| Cyclic scheduling | |
| Guttman scales | |
| Split Graphs | |
| Introduction | |
| Basic properties | |
| Hamiltonian split graphs | |
| The splittance of a graph | |
| The Threshold Dimension | |
| Introduction | |
| Bounds for the threshold dimension | |
| Dimensional properties | |
| Operations preserving the threshold dimension | |
| Restricted threshold dimension | |
| NP-Completeness | |
| Introduction | |
| The partial order dimension | |
| Related NP-complete problems | |
| Other complexity results | |
| The split dimension | |
| Polar graphs | |
| 2-Threshold Graphs | |
| Introduction | |
| Properties of 2-threshold graphs | |
| Bithreshold graphs | |
| Strict 2-threshold graphs | |
| Recognizing threshold dimension 2 | |
| Recognizing difference dimension 2 | |
| Intersection threshold dimension 2 | |
| The Dilworth Number | |
| Introduction | |
| Graphs of Dilworth number 2 | |
| The Dilworth number and perfect graphs | |
| Box-Threshold Graphs | |
| Introduction | |
| Elementary properties | |
| A transportation model | |
| Frames of BT graphs | |
| Matroidal and Matrogenic Graphs | |
| Introduction | |
| Matroidal graphs | |
| Matrogenic graphs | |
| Matrogenic sequences | |
| Domishold Graphs | |
| Introduction | |
| Notation and main results | |
| Equidominating graphs | |
| Pseudodomishold graphs | |
| The Decomposition Method | |
| Introduction | |
| The canonical decomposition | |
| Domishold graphs and decomposition | |
| Box-threshold graphs and decomposition | |
| Matroidal and matrogenic graphs and decomposition | |
| Pseudothreshold and Equistable Graphs | |
| Introduction | |
| Pseudothreshold graphs | |
| Equistable graphs | |
| Threshold Weights and Measures.Introduction | |
| Threshold weights | |
| Threshold measures | |
| Threshold and majorization gaps | |
| Threshold Graphs and Order Relations | |
| Introduction | |
| Biorders | |
| Bidimensions | |
| Relations of bidimension 2 | |
| Multiple semiorders | |
| Enumeration | |
| Introduction | |
| Enumeration of threshold graphs | |
| Enumeration of difference graphs | |
| Extremal Problems | |
| Introduction | |
| Large interval and threshold subgraphs of dense graphs | |
| Maximizing the sum of squares of degrees | |
| Other Extensions | |
| Introduction | |
| Geometric embeddings of graphs | |
| Tolerance intersection graphs | |
| Universal threshold graphs | |
| Bibliography | |
| List of Notations | |
| Author Index | |
| Index | |
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