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 decompos
Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.
The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field.
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- © North Holland 1995
- 13th September 1995
- North Holland
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Northeastern University, Department of Mathematics, Boston, MA, USA
The University of Illinois at Chicago, Department of Mathematics, Chicago, USA