COMBINATORICA
2007
13 years 7 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 7 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 7 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 7 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 7 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 7 months ago
2007
COMBINATORICA
2007
13 years 7 months ago
2007
COMBINATORICA
2007
13 years 7 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 7 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 7 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...