Partite construction and Ramseyan theorems for sets, numbers and spaces
Partitioning 3-colored complete graphs into three monochromatic cycles.
Paths and stability number in digraphs.
Planar Ramsey numbers
The planar Ramsey number PR(G,H) is defined as the smallest integer n for which any 2-colouring of edges of Kₙ with red and blue, where red edges induce a planar graph, leads to either a red copy of G, or a blue H. In this note we study the weak induced version of the planar Ramsey number in the case when the second graph is complete.
Problems on stars in complete graphs.
Proof of the conjecture for large .