| Preface | p. xiii |
| Introduction | p. 1 |
| Overview of graph coloring | p. 1 |
| Mixed hypergraphs and their coloring | p. 3 |
| Unforeseen features of mixed hypergraph coloring | p. 3 |
| Philosophical motivation of mixed hypergraph coloring | p. 4 |
| Organization | p. 5 |
| Acknowledgments | p. 9 |
| The Lower Chromatic Number of a Hypergraph | p. 11 |
| General concepts | p. 11 |
| A brief history of coloring theory | p. 16 |
| Basic results on hypergraph coloring | p. 19 |
| Hypertrees and chordal conformal hypergraphs | p. 23 |
| Mixed Hypergraphs and the Upper Chromatic Number | p. 27 |
| Basic definitions | p. 27 |
| Splitting-contraction algorithm | p. 30 |
| Basic properties of the upper chromatic number | p. 34 |
| Greedy C-hypergraph coloring algorithms | p. 37 |
| Algorithmic complexity | p. 42 |
| Open problems | p. 43 |
| Uncolorable Mixed Hypergraphs | p. 45 |
| Minimal uncolorable mixed hypergraphs | p. 45 |
| Uncolorability measures and a greedy algorithm | p. 48 |
| Colorability as an integer programming problem | p. 52 |
| Special types of uncolorable mixed hypergraphs | p. 54 |
| Open problems | p. 57 |
| Uniquely Colorable Mixed Hypergraphs | p. 59 |
| Preliminary | p. 59 |
| Embeddings into uc mixed hypergraphs | p. 60 |
| Separation using uc subhypergraphs | p. 61 |
| Recursive operations | p. 63 |
| Algorithmic complexity | p. 67 |
| UC mixed hypergraphs with x [greater than or equal] n - 2 | p. 67 |
| Uniquely colorable mixed hypertrees | p. 71 |
| Open problems | p. 76 |
| C-perfect Mixed Hypergraphs | p. 79 |
| Basic concepts | p. 79 |
| Minimal non-C-perfect mixed hypergraphs | p. 81 |
| C-perfection of mixed hypertrees | p. 84 |
| Algorithmic aspects of C-perfection | p. 85 |
| Open problems | p. 86 |
| Gaps in the Chromatic Spectrum | p. 89 |
| The smallest mixed hypergraphs with gaps | p. 89 |
| Feasible sets and a doubling-shifting algorithm | p. 91 |
| Smaller realization | p. 93 |
| 0-1 realization | p. 95 |
| Uniform bihypergraphs may have gaps | p. 96 |
| Separation on uc preserves continuity | p. 98 |
| Open problems | p. 99 |
| Interval Mixed Hypergraphs | p. 101 |
| Colorings | p. 101 |
| Linear time algorithm for the upper chromatic number | p. 104 |
| Chromatic spectrum is continuous | p. 105 |
| Open problems | p. 106 |
| Pseudo-chordal Mixed Hypergraphs | p. 107 |
| Preliminaries | p. 107 |
| Chromatic polynomial | p. 109 |
| Consequences and examples | p. 111 |
| A universal formula for chordal graphs | p. 115 |
| Open problems | p. 117 |
| Circular Mixed Hypergraphs | p. 119 |
| Preliminaries | p. 119 |
| Unique colorability, n even | p. 121 |
| Unique colorability, n odd | p. 123 |
| Colorability and lower chromatic number | p. 125 |
| Open problems | p. 127 |
| Planar Mixed Hypergraphs | p. 129 |
| Classic planar hypergraphs | p. 129 |
| Coloring bitriangulations | p. 130 |
| Bounds for the upper chromatic number | p. 135 |
| Gaps in the chromatic spectrum | p. 137 |
| Open problems | p. 138 |
| Coloring Block Designs as Mixed Hypergraphs | p. 141 |
| Steiner systems | p. 141 |
| Steiner triple systems | p. 143 |
| Steiner quadruple systems | p. 149 |
| Open problems | p. 153 |
| Modelling with Mixed Hypergraphs | p. 155 |
| List colorings without lists | p. 155 |
| Ramsey, anti-Ramsey and related problems | p. 156 |
| Mixed hypergraphs and integer programming | p. 158 |
| Resource allocation | p. 162 |
| Lifetime of set systems | p. 165 |
| Parallel computing | p. 165 |
| Database management | p. 165 |
| Molecular biology | p. 166 |
| Genetics of populations | p. 168 |
| Natural number interpretation | p. 169 |
| Bibliography | p. 171 |
| List of Figures | p. 179 |
| Index | p. 181 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
