Convexity and Graph Theory

Front Cover
M. Rosenfeld, J. Zaks
Elsevier, Jan 1, 1984 - Mathematics - 338 pages
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Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings 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'', ``Weakly 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.

 

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Contents

Chapter 1 On extreme positive operators between polyhedral cones
1
Chapter 2 Miscellaneous properties of equieccentric graphs
13
Chapter 3 On the number of subgraphs of prescribed type of planar graphs with a given number of vertices
25
Chapter 4 Some conditions for digraphs to be Hamiltonian
37
Chapter 5 Covering of vertices of a simple graph with given connectivity and stability number
43
Chapter 6 Embedding Latin squares in Steiner quasigroups and Howell designs in triple systems
47
Chapter 7 Convexity graph theory and nonnegative matrices
55
Chapter 8 Lattice points and lattice polytopes
61
Chapter 26 Additive sequences of permutations
197
Chapter 27 On pairs of disjoint segments in convex position in the plane
203
Chapter 28 The decomposition of the nsphere and the boundaries of plane convex domains
209
Chapter 29 Bounding the numbers of faces of polytope pairs and simple polyhedra
215
Chapter 30 Parity in the realm of infinite permutations
233
Chapter 31 NonHamiltonian simple 3polytopes with only one type of face besides triangles
241
Chapter 32 At most 2d+1 neighborly simplices in Ed
253
Chapter 33 Some recent results on cycle traversability in graphs
255

Chapter 9 A new upper bound for the cardinality of 2distance sets in Euclidean space
65
Chapter 10 Geodesics in oriented graphs
67
Chapter 11 Recent results on the Strong Perfect Graph Conjecture
75
Chapter 12 Iterative methods for the convex feasibility problem
83
Chapter 13 Inequalities involving convex sets and their chords
93
Chapter 14 A symmetrical arrangement of eleven hemiicosahedra
103
Chapter 15 Regular incidencecomplexes and dimensionally unbounded sequences of such I
115
Chapter 16 Some old and new problems in combinatorial geometry
129
Chapter 17 PseudoBoolean functions and their graphs
137
Chapter 18 Valuations of trees polynomial equations and polytopes
147
Chapter 19 Spectra of trees
151
Chapter 20 The valencefunctional
161
Chapter 21 Matroids with weighted bases and Feynman integrals
165
Chapter 22 Balanced pairs
177
Chapter 23 On automorphisms of graphs with forbidden subgraphs
183
Chapter 24 Weakly saturated graphs are rigid
189
Chapter 25 Decomposability of polytopes is a projective invariant
191
Chapter 34 Generalized Hamiltonian paths in tournaments
263
Chapter 35 Large regular factors in random graphs
271
Chapter 36 Techniques for investigating neighborly polytopes
283
Chapter 37 Exchange properties of convexity spaces
293
Hensleys lattice polytope theorem
307
Chapter 39 Intersecting diameters in convex bodies
311
Chapter 40 Quadratic forms and graphs Abstract
317
Chapter 41 Approximation of convex bodies by polytopes with uniformly bounded valences Abstract
319
Chapter 42 Some results on convexity in graphs Abstract
321
Achievement and avoidance games Abstract
323
Chapter 44 On scheduling the construction of a tree Abstract
325
Chapter 45 Edge maps and isomorphisms of graphs Abstract
327
Chapter 46 A multiflow problem without the maxflow mincut property Abstract
329
Chapter 47 Polyhedral manifolds with few vertices Abstract
331
Chapter 48 Regular polyhedral manifolds Abstract
333
Open problems
335
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