Arranging Points in Rd̳: A Question of Balance |
Contents
A survey of some related works | 13 |
Notation and remarks | 21 |
Two graph theory problems as special cases | 64 |
1 other sections not shown
Common terms and phrases
3-circuits B₁ B₁(P balancing problem bound 2d C₁ chromatic number problem cocircuit space color column vectors complete graph completes the proof configuration in Rd consider contains the origin conv(A convex hull Corollary corresponding d-dimensional decomposition defined Denote directed circuit directed graph elementary vectors ENGINEERING LIBRARY equivalent Euclidean example finite nondegenerate configuration finite set finite subset G is k-colorable graph G graph theory H contains H₁ Hence hyperplane hyperplane H incidence matrix incidence vector integer flow k-colorable K₁ Lemma linear spaces linear subspace linearly independent nonzero vector norm NP-complete ordering orientation of G oriented matroid P₁ partial sums perfect matching points polynomial positive integer procedure proof of Theorem real number row space row vectors S+(x S₁ satisfies signed sets Spencer ẞ₁(P strongly connected components Suppose supremum totally unimodular matrix two-coloring U₁ vertex vertex-edge incidence matrix vertices X₁ Y₁ y₁(P