Graph Theory » Coloring » Vertex coloring

List Hadwiger Conjecture ★★

Author(s): Kawarabayashi; Mohar

Conjecture   Every $ K_t $-minor-free graph is $ c t $-list-colourable for some constant $ c\geq1 $.

Keywords: Hadwiger conjecture; list colouring; minors

Posted by David Wood
updated July 7th, 2014
add new comment
Topology

Coatoms of the lattice of funcoids ★

Author(s): Porton

Problem   Let $ A $ and $ B $ be infinite sets. Characterize the set of all coatoms of the lattice $ \mathsf{FCD}(A;B) $ of funcoids from $ A $ to $ B $. Particularly, is this set empty? Is $ \mathsf{FCD}(A;B) $ a coatomic lattice? coatomistic lattice?

Keywords: atoms; coatoms; funcoids

Posted by porton
updated April 24th, 2014
add new comment