ZFC


ZF


Graph Theory » Basic G.T.

Almost all non-Hamiltonian 3-regular graphs are 1-connected ★★

Author(s): Haythorpe

Conjecture   Denote by $ NH(n) $ the number of non-Hamiltonian 3-regular graphs of size $ 2n $, and similarly denote by $ NHB(n) $ the number of non-Hamiltonian 3-regular 1-connected graphs of size $ 2n $.

Is it true that $ \lim\limits_{n \rightarrow \infty} \displaystyle\frac{NHB(n)}{NH(n)} = 1 $?

Keywords: Hamiltonian, Bridge, 3-regular, 1-connected

Posted by mhaythorpe
updated August 23rd, 2013
add new comment
Graph Theory » Coloring » Vertex coloring

Erdős–Faber–Lovász conjecture ★★★

Author(s): Erdos; Faber; Lovasz

Conjecture   If $ G $ is a simple graph which is the union of $ k $ pairwise edge-disjoint complete graphs, each of which has $ k $ vertices, then the chromatic number of $ G $ is $ k $.

Keywords: chromatic number

Posted by Jon Noel
updated August 22nd, 2013
add new comment