Gluck [6] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K5-minor freeness gua...
For a given graph G = (V, E) and a positive integer k, the super line graph of index k of G is the graph Sk(G) which has for vertices all the k-subsets of E(G), and two vertices S...
Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint sub...
It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at l...
We introduce and analyze σ-local graphs, based on a definition of locality by Erickson [12]. We present two algorithms to construct such graphs, for any real number σ > 1 an...