
Recent Activity
Big Line or Big Clique in Planar Point Sets ★★
Let be a set of points in the plane. Two points
and
in
are visible with respect to
if the line segment between
and
contains no other point in
.





Keywords: Discrete Geometry; Geometric Ramsey Theory
Mixing Circular Colourings ★

Keywords: discrete homotopy; graph colourings; mixing
The Borodin-Kostochka Conjecture ★★


Keywords:
Chromatic number of random lifts of complete graphs ★★
Author(s): Amit

Keywords: random lifts, coloring
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime ★★
Author(s):
Keywords:
Circular choosability of planar graphs ★
Author(s): Mohar
Let be a graph. If
and
are two integers, a
-colouring of
is a function
from
to
such that
for each edge
. Given a list assignment
of
, i.e.~a mapping that assigns to every vertex
a set of non-negative integers, an
-colouring of
is a mapping
such that
for every
. A list assignment
is a
-
-list-assignment if
and
for each vertex
. Given such a list assignment
, the graph G is
-
-colourable if there exists a
-
-colouring
, i.e.
is both a
-colouring and an
-colouring. For any real number
, the graph
is
-
-choosable if it is
-
-colourable for every
-
-list-assignment
. Last,
is circularly
-choosable if it is
-
-choosable for any
,
. The circular choosability (or circular list chromatic number or circular choice number) of G is
Keywords: choosability; circular colouring; planar graphs
A conjecture about direct product of funcoids ★★
Author(s): Porton







A positive solution of this problem may open a way to prove that some funcoids-related categories are cartesian closed.
Keywords: category theory; general topology
MacEachen Conjecture ★
Author(s): McEachen
Keywords: primality; prime distribution
Criterion for boundedness of power series ★
Author(s): Rüdinger



Keywords: boundedness; power series; real analysis
Length of surreal product ★
Author(s): Gonshor





It is easy to prove that
What about
?
Keywords: surreal numbers
Durer's Conjecture ★★★
Convex uniform 5-polytopes ★★
Author(s):
Keywords:
MSO alternation hierarchy over pictures ★★
Author(s): Grandjean
Keywords: FMT12-LesHouches; MSO, alternation hierarchy; picture languages
Blatter-Specker Theorem for ternary relations ★★
Author(s): Makowsky
Let be a class of finite relational structures. We denote by
the number of structures in
over the labeled set
. For any class
definable in monadic second-order logic with unary and binary relation symbols, Specker and Blatter showed that, for every
, the function
is ultimately periodic modulo
.
Keywords: Blatter-Specker Theorem; FMT00-Luminy
Monadic second-order logic with cardinality predicates ★★
Author(s): Courcelle
The problem concerns the extension of Monadic Second Order Logic (over a binary relation representing the edge relation) with the following atomic formulas:
- \item


where is a fixed recursive set of integers.
Let us fix and a closed formula
in this language.




Keywords: bounded tree width; cardinality predicates; FMT03-Bedlewo; MSO
Order-invariant queries ★★
Author(s): Segoufin
- \item Does






Keywords: Effective syntax; FMT12-LesHouches; Locality; MSO; Order invariance
Fixed-point logic with counting ★★
Author(s): Blass
- \item Given a graph, does it have a perfect matching, i.e., a set


Keywords: Capturing PTime; counting quantifiers; Fixed-point logic; FMT03-Bedlewo
Birch & Swinnerton-Dyer conjecture ★★★★
Author(s):






Keywords:
Is Skewes' number e^e^e^79 an integer? ★★
Author(s):
Skewes' number is not an integer.
Keywords: