Recent Activity
The intersection of two perfect matchings ★★
Keywords: cubic; nowhere-zero flow; perfect matching
Counterexamples to the Baillie-PSW primality test ★★
Author(s):
Keywords:
A sextic counterexample to Euler's sum of powers conjecture ★★
Author(s): Euler
Keywords:
Geodesic cycles and Tutte's Theorem ★★
Author(s): Georgakopoulos; Sprüssel
Keywords: cycle space; geodesic cycles; peripheral cycles
Oriented chromatic number of planar graphs ★★
Author(s):
An oriented colouring of an oriented graph is assignment of colours to the vertices such that no two arcs receive ordered pairs of colours and . It is equivalent to a homomorphism of the digraph onto some tournament of order .
Keywords: oriented coloring; oriented graph; planar graph
Covering systems with big moduli ★★
Keywords: covering system
Odd incongruent covering systems ★★★
Keywords: covering system
Hamiltonian cycles in powers of infinite graphs ★★
Author(s): Georgakopoulos
- \item If is a countable connected graph then its third power is hamiltonian. \item If is a 2-connected countable graph then its square is hamiltonian.
Keywords: hamiltonian; infinite graph
Hamiltonian cycles in line graphs of infinite graphs ★★
Author(s): Georgakopoulos
- \item If is a 4-edge-connected locally finite graph, then its line graph is hamiltonian. \item If the line graph of a locally finite graph is 4-connected, then is hamiltonian.
Keywords: hamiltonian; infinite graph; line graphs
Hamiltonian cycles in line graphs ★★★
Author(s): Thomassen
Keywords: hamiltonian; line graphs
Infinite uniquely hamiltonian graphs ★★
Author(s): Mohar
Keywords: hamiltonian; infinite graph; uniquely hamiltonian
Linear-size circuits for stable $0,1 < 2$ sorting? ★★
Author(s): Regan
Unconditional derandomization of Arthur-Merlin games ★★★
Keywords: Arthur-Merlin; Hitting Sets; unconditional
Subset-sums equality (pigeonhole version) ★★★
Author(s):
Keywords: polynomial algorithm; search problem
Weak pentagon problem ★★
Author(s): Samal
Keywords: Clebsch graph; cut-continuous mapping; edge-coloring; homomorphism; pentagon
Lonely runner conjecture ★★★
Keywords: diophantine approximation; view obstruction
Mapping planar graphs to odd cycles ★★★
Author(s): Jaeger
Keywords: girth; homomorphism; planar graph
5-local-tensions ★★
Author(s): DeVos
Concavity of van der Waerden numbers ★★
Author(s): Landman
For and positive integers, the (mixed) van der Waerden number is the least positive integer such that every (red-blue)-coloring of admits either a -term red arithmetic progression or an -term blue arithmetic progression.
Keywords: arithmetic progression; van der Waerden
Circular coloring triangle-free subcubic planar graphs ★★
Keywords: circular coloring; planar graph; triangle free