Recent Activity
List colorings of edge-critical graphs ★★
Author(s): Mohar
Keywords: edge-coloring; list coloring
Aharoni-Berger conjecture ★★★
Keywords: independent set; matroid; partition
The large sets conjecture ★★★
Author(s): Brown; Graham; Landman
Keywords: 2-large sets; large sets
Ramsey properties of Cayley graphs ★★★
Author(s): Alon
Keywords: Cayley graph; Ramsey number
Bases of many weights ★★★
Let be an (additive) abelian group, and for every let .
The Erdos-Turan conjecture on additive bases ★★★★
Let . The representation function for is given by the rule . We call an additive basis if is never .
Keywords: additive basis; representation function
Rota's unimodal conjecture ★★★
Author(s): Rota
Let be a matroid of rank , and for let be the number of closed sets of rank .
Keywords: flat; log-concave; matroid
A conjecture on iterated circumcentres ★★
Author(s): Goddyn
Keywords: periodic; plane geometry; sequence
Unions of triangle free graphs ★★★
Keywords: forbidden subgraph; infinite graph; triangle free
The Two Color Conjecture ★★
Author(s): Neumann-Lara
Half-integral flow polynomial values ★★
Author(s): Mohar
Let be the flow polynomial of a graph . So for every positive integer , the value equals the number of nowhere-zero -flows in .
Keywords: nowhere-zero flow
Gao's theorem for nonabelian groups ★★
Author(s): DeVos
For every finite multiplicative group , let () denote the smallest integer so that every sequence of elements of has a subsequence of length (length ) which has product equal to 1 in some order.
Keywords: subsequence sum; zero sum
Universal point sets for planar graphs ★★★
Author(s): Mohar
We say that a set is -universal if every vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in , and all edges are (non-intersecting) straight line segments.
Keywords: geometric graph; planar graph; universal set
Antichains in the cycle continuous order ★★
Author(s): DeVos
If , are graphs, a function is called cycle-continuous if the pre-image of every element of the (binary) cycle space of is a member of the cycle space of .
Fat 4-polytopes ★★★
Author(s): Eppstein; Kuperberg; Ziegler
The fatness of a 4-polytope is defined to be where is the number of faces of of dimension .
The Crossing Number of the Complete Bipartite Graph ★★★
Author(s): Turan
The crossing number of is the minimum number of crossings in all drawings of in the plane.
Keywords: complete bipartite graph; crossing number
Woodall's Conjecture ★★★
Author(s): Woodall
Pentagon problem ★★★
Author(s): Nesetril
Keywords: cubic; homomorphism
Ryser's conjecture ★★★
Author(s): Ryser
Keywords: hypergraph; matching; packing
The Erdös-Hajnal Conjecture ★★★
Keywords: induced subgraph