4 papers
On a problem of Caro on -Ramsey number of forests
José D. Alvarado, Lucas Colucci, Roberto Parente
Let be a positive integer and let be a graph. The zero-sum Ramsey number is the least integer (if it exists) such that for every edge-coloring $Ï\,…
A canonical Ramsey theorem for even cycles in random graphs
José D. Alvarado, Y. Kohayakawa, Patrick Morris +1
The celebrated canonical Ramsey theorem of ErdÅs and Rado implies that for , any colouring of the edges of with sufficiently large gives a copy of…
A sparse canonical van der Waerden theorem
José D. Alvarado, Yoshiharu Kohayakawa, Patrick Morris +2
The canonical van der Waerden theorem asserts that, for sufficiently large , every colouring of contains either a monochromatic or a rainbow arithmetic progression of leng…
A canonical Ramsey theorem with list constraints in random (hyper-)graphs
José D. Alvarado, Yoshiharu Kohayakawa, Patrick Morris +1
The celebrated canonical Ramsey theorem of ErdÅs and Rado implies that for a given -uniform hypergraph (or -graph) , if is sufficiently large then any colouring of th…