简介
Among the participants discussing recent trends in their respective fields and in areas of common interest in theseproceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ??Convexity, Graph Theory and Non-Negative Matrices'', ??eakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
目录
Contents 8
Preface 6
List of participants 11
Chapter 1. On extreme positive operators between polyhedral cones 14
Chapter 2. Miscellaneous properties of equieccentric graphs 26
Chapter 3. On the number of subgraphs of prescribed type of planar graphs with a given number of vertices 38
Chapter 4. Some conditions for digraphs to be Hamiltonian 50
Chapter 5. Covering of vertices of a simple graph with given connectivity and stability number 56
Chapter 6. Embedding Latin squares in Steiner quasigroups, and Howell designs in triple systems 60
Chapter 7. Convexity, graph theory and non-negative matrices 68
Chapter 8. Lattice points and lattice polytopes 74
Chapter 9. A new upper bound for the cardinality of 2-distance sets in Euclidean space 78
Chapter 10. Geodesics in oriented graphs 80
Chapter 11. Recent results on the Strong Perfect Graph Conjecture 88
Chapter 12. Iterative methods for the convex feasibility problem 96
Chapter 13. Inequalities involving convex sets and their chords 106
Chapter 14. A symmetrical arrangement of eleven hemi-icosahedra 116
Chapter 15. Regular incidence-complexes and dimensionally unbounded sequences of such, I 128
Chapter 16. Some old and new problems in combinatorial geometry 142
Chapter 17. Pseudo-Boolean functions and their graphs 150
Chapter 18. Valuations of trees, polynomial equations and polytopes 160
Chapter 19. Spectra of trees 164
Chapter 20. The valence-functional 174
Chapter 21. Matroids with weighted bases and Feynman integrals 178
Chapter 22. Balanced pairs 190
Chapter 23. On automorphisms of graphs with forbidden subgraphs 196
Chapter 24. Weakly saturated graphs are rigid 202
Chapter 25. Decomposability of polytopes is a projective invariant 204
Chapter 26. Additive sequences of permutations 210
Chapter 27. On pairs of disjoint segments in convex position in the plane 216
Chapter 28. The decomposition of the n-sphere and the boundaries of plane convex domains 222
Chapter 29. Bounding the numbers of faces of polytope pairs and simple polyhedra 228
Chapter 30. Parity in the realm of infinite permutations 246
Chapter 31. Non-Hamiltonian simple 3-polytopes with only one type of face besides triangles 254
Chapter 32. At most 2d+1 neighborly simplices in Ed 266
Chapter 33. Some recent results on cycle traversability in graphs 268
Chapter 34. Generalized Hamiltonian paths in tournaments 276
Chapter 35. Large regular factors in random graphs 284
Chapter 36. Techniques for investigating neighborly polytopes 296
Chapter 37. Exchange properties of convexity spaces 306
Chapter 38. Extending Kotzig's Theorem: Hensley's lattice polytope theorem 320
Chapter 39. Intersecting diameters in convex bodies 324
Chapter 40. Quadratic forms and graphs (Abstract) 330
Chapter 41. Approximation of convex bodies by polytopes with uniformly bounded valences (Abstract) 332
Chapter 42. Some results on convexity in graphs (Abstract) 334
Chapter 43. Convexity in graphs: Achievement and avoidance games (Abstract) 336
Chapter 44. On scheduling the construction of a tree (Abstract) 338
Chapter 45. Edge maps and isomorphisms of graphs (Abstract) 340
Chapter 46. A multiflow problem without the max-flow min-cut property (Abstract) 342
Chapter 47. Polyhedral manifolds with few vertices (Abstract) 344
Chapter 48. Regular polyhedral manifolds (Abstract) 346
Open problems 348
Preface 6
List of participants 11
Chapter 1. On extreme positive operators between polyhedral cones 14
Chapter 2. Miscellaneous properties of equieccentric graphs 26
Chapter 3. On the number of subgraphs of prescribed type of planar graphs with a given number of vertices 38
Chapter 4. Some conditions for digraphs to be Hamiltonian 50
Chapter 5. Covering of vertices of a simple graph with given connectivity and stability number 56
Chapter 6. Embedding Latin squares in Steiner quasigroups, and Howell designs in triple systems 60
Chapter 7. Convexity, graph theory and non-negative matrices 68
Chapter 8. Lattice points and lattice polytopes 74
Chapter 9. A new upper bound for the cardinality of 2-distance sets in Euclidean space 78
Chapter 10. Geodesics in oriented graphs 80
Chapter 11. Recent results on the Strong Perfect Graph Conjecture 88
Chapter 12. Iterative methods for the convex feasibility problem 96
Chapter 13. Inequalities involving convex sets and their chords 106
Chapter 14. A symmetrical arrangement of eleven hemi-icosahedra 116
Chapter 15. Regular incidence-complexes and dimensionally unbounded sequences of such, I 128
Chapter 16. Some old and new problems in combinatorial geometry 142
Chapter 17. Pseudo-Boolean functions and their graphs 150
Chapter 18. Valuations of trees, polynomial equations and polytopes 160
Chapter 19. Spectra of trees 164
Chapter 20. The valence-functional 174
Chapter 21. Matroids with weighted bases and Feynman integrals 178
Chapter 22. Balanced pairs 190
Chapter 23. On automorphisms of graphs with forbidden subgraphs 196
Chapter 24. Weakly saturated graphs are rigid 202
Chapter 25. Decomposability of polytopes is a projective invariant 204
Chapter 26. Additive sequences of permutations 210
Chapter 27. On pairs of disjoint segments in convex position in the plane 216
Chapter 28. The decomposition of the n-sphere and the boundaries of plane convex domains 222
Chapter 29. Bounding the numbers of faces of polytope pairs and simple polyhedra 228
Chapter 30. Parity in the realm of infinite permutations 246
Chapter 31. Non-Hamiltonian simple 3-polytopes with only one type of face besides triangles 254
Chapter 32. At most 2d+1 neighborly simplices in Ed 266
Chapter 33. Some recent results on cycle traversability in graphs 268
Chapter 34. Generalized Hamiltonian paths in tournaments 276
Chapter 35. Large regular factors in random graphs 284
Chapter 36. Techniques for investigating neighborly polytopes 296
Chapter 37. Exchange properties of convexity spaces 306
Chapter 38. Extending Kotzig's Theorem: Hensley's lattice polytope theorem 320
Chapter 39. Intersecting diameters in convex bodies 324
Chapter 40. Quadratic forms and graphs (Abstract) 330
Chapter 41. Approximation of convex bodies by polytopes with uniformly bounded valences (Abstract) 332
Chapter 42. Some results on convexity in graphs (Abstract) 334
Chapter 43. Convexity in graphs: Achievement and avoidance games (Abstract) 336
Chapter 44. On scheduling the construction of a tree (Abstract) 338
Chapter 45. Edge maps and isomorphisms of graphs (Abstract) 340
Chapter 46. A multiflow problem without the max-flow min-cut property (Abstract) 342
Chapter 47. Polyhedral manifolds with few vertices (Abstract) 344
Chapter 48. Regular polyhedral manifolds (Abstract) 346
Open problems 348
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