Contents -- Preface -- Introduction -- Chapter 1 Contributions of F.R. McMorris to Character Compatibility Analysis -- Introduction -- 1.1. Basic Concepts -- 1.2. Potential Compatibility Algorithm -- 1.3. Applications of Compatibility using McMorris' Results -- 1.4. Possible Future Applications -- References -- Chapter 2 Families of Relational Statistics for 2 x 2 Tables -- Introduction -- 2.1. Definitions -- 2.1.1. Preliminaries -- 2.1.2. Type A statistics -- 2.1.3. Type B statistics -- 2.1.4. Type C statistics -- 2.2. Examples of relational statistics for 2 x 2 tables -- 2.2.1. Tetrachoric correlation and odds ratio -- 2.2.2. Epidemiological studies -- 2.2.3. Ecological association -- 2.2.4. Comparing two partitions -- 2.2.5. Test homogeneity -- 2.3. Families of relational statistics for 2 x 2 tables -- 2.3.1. Rational functions -- 2.3.2. Chance-corrected statistics -- 2.3.3. Power mean -- 2.3.4. Linear transformations of SSM -- 2.4. Discussion -- 2.4.1. Order equivalence -- 2.4.2. Inequalities -- 2.4.3. Correction for chance -- 2.4.4. Correction for maximum value -- References -- Chapter 3 Applications of Spanning Subgraphs of Intersection Graphs -- Introduction -- 3.1. A Family-Tree Approach to Graph Classes -- 3.1.1. Basic results on F-tree representations -- 3.1.2. F-tree representations for chordal graphs -- 3.1.3. F-tree representations for other graph classes -- 3.1.4. F-tree representations for distance-hereditary graph -- 3.1.5. Returning to the molecular biology example -- 3.1.6. More general F-graph representations -- 3.2. Hunter-Worsley/Bonferroni-Type Set Bounds -- 3.2.1. Several classical set bounds -- 3.2.2. Two 2-tree versions of the Hunter-Worsley bound -- 3.2.3. The chordal graph sieve -- 3.2.4. Economical inclusion-exclusion -- References -- Chapter 4 Axiomatic Characterization of Location Functions -- Introduction.

4.1. The model -- 4.2. Basic Axioms -- 4.3. The Center Function -- 4.4. The median Function -- 4.4.1. The Median Function on Median Graphs -- 4.4.2. The t-Median Function on Median Semilattices -- 4.4.3. The Median Function on Cube-free Median Networks -- 4.5. The Mean Function on Trees -- 4.6. Concluding Remarks -- References -- Chapter 5 Median Graphs. A Structure Theory -- Introduction -- 5.1. Definitions and Preliminaries -- 5.2. The Expansion Theorem -- 5.3. The Armchair -- 5.4. Median Sets in Median Graphs -- 5.5. Median Graphs in the Mathematical Universe -- 5.6. Median Structures -- 5.6.1. Ternary algebras -- 5.6.2. Betweenness -- 5.6.3. Semilattices -- 5.6.4. Hypergraphs and convexities -- 5.6.5. Join geometries -- 5.6.6. Conflict models -- 5.6.7. Transit Functions -- 5.7. Generalizations -- 5.7.1. Quasi-median Graphs -- 5.7.2. Expansions -- 5.7.3. Retracts -- 5.7.4. Median-type Graphs -- 5.7.5. Transit Functions -- 5.8. Applications -- 5.8.1. Location Theory -- 5.8.2. Consensus Functions -- 5.8.3. Chemistry -- 5.8.4. Biology and Psychology -- 5.8.5. Literary History -- 5.8.6. Economics and Voting Theory -- 5.9. Concluding Remarks -- References -- Chapter 6 Generalized Centrality in Trees -- Introduction -- 6.1. Preliminaries -- 6.2. Generalized path centers and path centroids -- 6.3. Generalized path medians -- 6.4. Conclusions -- Acknowledgements -- References -- Chapter 7 Consensus Centered at Majority Rule -- Introduction -- 7.1. The Monjardet Model of Consensus -- 7.2. Absolute Majority Rules -- 7.3. Social Welfare Functions -- 7.4. Conclusion -- References -- Chapter 8 Centrality Measures in Trees -- Introduction -- 8.1. The Center -- 8.2. The Median -- 8.3. Two more central sets that induce K1 or K2 -- 8.4. Families of central sets inducing K1 or K2 -- 8.5. Central subtrees -- 8.6. Disconnected central sets.

8.7. Connected central structures -- References -- Chapter 9 The Port Reopening Scheduling Problem -- Introduction -- 9.1. Formalizing the Problem -- 9.2. Penalty Functions -- 9.3. The Case of Common Desired Arrival Times -- 9.4. Nonconstant Desired Arrival Times -- 9.5. Meaningful Conclusions -- 9.6. Closing Comments -- References -- Chapter 10 Reexamining the Complexities in Consensus Theory -- 10.1. The problem -- 10.2. Arrow's Theorem and surprising extensions -- 10.3. Still another vote -- 10.4. Finding the actual space of inputs -- 10.4.1. Outline of Arrow's result where "involvement" replaces Pareto -- 10.4.2. Finding the problem -- 10.4.3. Other compatibility and independence conditions -- 10.4.4. Positive conclusions? -- 10.5. Summary -- References -- Chapter 11 The Contributions of F.R. McMorris to Discrete Mathematics and its Applications -- Introduction -- 11.1. Mathematics of Evolutionary Biology -- 11.2. Contributions to Intersection Graph Theory -- 11.3. Competition Graphs and their Generalizations -- 11.3.1. Competition Graph Definitions and Applications -- 11.3.2. Competition Numbers and Phylogeny Numbers -- 11.3.3. p-Competition Graphs -- 11.3.4. Tolerance Competition Graphs -- 11.4. Location Functions on Graphs -- 11.5. Contributions to Bioconsensus: An Axiomatic Approach -- References -- Author Index -- Subject Index -- Symbol Index.