
Monotone 4-term Arithmetic Progressions ★★
Author(s): Davis; Entringer; Graham; Simmons
Question Is it true that every permutation of positive integers must contain monotone 4-term arithmetic progressions?
Keywords: monotone arithmetic progression; permutation
Coloring the Odd Distance Graph ★★★
Author(s): Rosenfeld
The Odd Distance Graph, denoted , is the graph with vertex set
and two points adjacent if the distance between them is an odd integer.
Question Is
?

Keywords: coloring; geometric graph; odd distance
The Bermond-Thomassen Conjecture ★★
Conjecture For every positive integer
, every digraph with minimum out-degree at least
contains
disjoint cycles.



Keywords: cycles