JCT
2006
13 years 9 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 9 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 9 months ago
2006
JCT
2006
13 years 9 months ago
2006
JCT
2006
13 years 9 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 9 months ago
2006
JCT
2006
13 years 9 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 9 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 9 months ago
2006
The Frankl-R
JCT
2006
13 years 9 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...