
Recent Activity
Chromatic number of $\frac{3}{3}$-power of graph ★★
Author(s):
Let be a graph and
. The graph
is defined to be the
-power of the
-subdivision of
. In other words,
.



Keywords:
3-Edge-Coloring Conjecture ★★★
Author(s): Arthur; Hoffmann-Ostenhof






Keywords: 3-edge coloring; 4-flow; removable edge
r-regular graphs are not uniquely hamiltonian. ★★★
Author(s): Sheehan




Keywords: hamiltonian; regular; uniquely hamiltonian
Partition of Complete Geometric Graph into Plane Trees ★★
Author(s):
Keywords: complete geometric graph, edge colouring
Smooth 4-dimensional Poincare conjecture ★★★★
Author(s): Poincare; Smale; Stallings




Keywords: 4-manifold; poincare; sphere
Book Thickness of Subdivisions ★★
Author(s): Blankenship; Oporowski
Let be a finite undirected simple graph.
A -page book embedding of
consists of a linear order
of
and a (non-proper)
-colouring of
such that edges with the same colour do not cross with respect to
. That is, if
for some edges
, then
and
receive distinct colours.
One can think that the vertices are placed along the spine of a book, and the edges are drawn without crossings on the pages of the book.
The book thickness of , denoted by bt
is the minimum integer
for which there is a
-page book embedding of
.
Let be the graph obtained by subdividing each edge of
exactly once.



Keywords: book embedding; book thickness
Primitive pythagorean n-tuple tree ★★
Author(s):
Keywords:
Jacobian Conjecture ★★★
Author(s): Keller




Keywords: Affine Geometry; Automorphisms; Polynomials
Inscribed Square Problem ★★
Author(s): Toeplitz
Keywords: simple closed curve; square
Complete bipartite subgraphs of perfect graphs ★★
Author(s): Fox






Keywords: perfect graph
Transversal achievement game on a square grid ★★
Author(s): Erickson


Keywords: game
Graceful Tree Conjecture ★★★
Author(s):
Keywords: combinatorics; graceful labeling
Extremal problem on the number of tree endomorphism ★★
Author(s): Zhicong Lin



Keywords:
3-Colourability of Arrangements of Great Circles ★★
Author(s): Felsner; Hurtado; Noy; Streinu
Consider a set of great circles on a sphere with no three circles meeting at a point. The arrangement graph of
has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points. So this arrangement graph is 4-regular and planar.

Keywords: arrangement graph; graph coloring
KPZ Universality Conjecture ★★★
Author(s):
Keywords: KPZ equation, central limit theorem
Friendly partitions ★★
Author(s): DeVos
A friendly partition of a graph is a partition of the vertices into two sets so that every vertex has at least as many neighbours in its own class as in the other.


Finite entailment of Positive Horn logic ★★
Author(s): Martin


Keywords: entailment; finite satisfiability; horn logic
Triangle free strongly regular graphs ★★★
Author(s):
Keywords: strongly regular; triangle free
A discrete iteration related to Pierce expansions ★★
Author(s): Shallit






Example: , since
,
,
,
,
,
,
,
.
Prove or disprove: .
Keywords: Pierce expansions
Bounding the chromatic number of triangle-free graphs with fixed maximum degree ★★


Keywords: chromatic number; girth; maximum degree; triangle free