COMBINATORICA
2007
13 years 11 months ago
2007
A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a ...
COMBINATORICA
2007
13 years 11 months ago
2007
The main result of this paper is that every 4-uniform hypergraph on n vertices and m edges has a transversal with no more than (5n + 4m)/21 vertices. In the particular case n = m,...
COMBINATORICA
2007
13 years 11 months ago
2007
We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1 − )n vertices, in terms of the expansion prop...
COMBINATORICA
2007
13 years 11 months ago
2007
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...
COMBINATORICA
2007
13 years 11 months ago
2007
A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that ...
COMBINATORICA
2007
13 years 11 months ago
2007
COMBINATORICA
2007
13 years 11 months ago
2007
COMBINATORICA
2007
13 years 11 months ago
2007
The standard Erd˝os-Renyi model of random graphs begins with n isolated vertices, and at each round a random edge is added. Parametrizing n 2 rounds as one time unit, a phase tra...
COMBINATORICA
2007
13 years 11 months ago
2007
The k-th power of a graph G is the graph whose vertex set is V (G)k , where two distinct ktuples are adjacent iff they are equal or adjacent in G in each coordinate. The Shannon ...
COMBINATORICA
2007
13 years 11 months ago
2007
What is the maximum possible number, f3(n), of vectors of length n over {0, 1, 2} such that the Hamming distance between every two is even? What is the maximum possible number, g3...