JGT
2010
13 years 3 months ago
2010
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. In this paper we prove a weakened version of this conjecture for the class ...
JCT
2006
13 years 4 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...
DM
2006
13 years 4 months ago
2006
Let G be a connected, locally connected, claw-free graph of order n and x, y be two vertices of G. In this paper, we prove that if for any 2-cut S of G, S {x, y} = , then each (x...