JCT
2006
13 years 11 months ago
2006
We prove that an excluded minor for the class of GF(q)-representable matroids cannot contain a large projective geometry over GF(q) as a minor.
JCT
2006
13 years 11 months ago
2006
Thomassen conjectured that every 4-connected line graph is hamiltonian. A vertex cut X of G is essential if G-X has at least two nontrivial components. We prove that every 3-conne...
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f ) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2,3 (Bender and Canf...
JCT
2006
13 years 11 months ago
2006
JCT
2006
13 years 11 months ago
2006
Consider two locally finite rooted trees as equivalent if each of them is a topological minor of the other, with an embedding preserving the tree-order. Answering a question of va...
JCT
2006
13 years 11 months ago
2006
A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. A brick is minimal if for every edge e the deletio...
JCT
2006
13 years 11 months ago
2006
The Frankl-R
JCT
2006
13 years 11 months ago
2006
Fix positive integers k , d , k, d such that k /d > k/d 2. If P is a set of vertices in a (k, d)-colorable graph G, and any two vertices of P are separated by distance at leas...