Motivated by an extremal problem on graph-codes that links coding theory and
graph theory, Alon recently proposed a question aiming to find the smallest
number t such that there is an edge coloring of Knβ by t colors with no
copy of given graph H in which every color appears an even number of times.
When H=K4β, the question of whether no(1) colors are enough, was
initially emphasized by Alon. Through modifications to the coloring functions
originally designed by Mubayi, and Conlon, Fox, Lee and Sudakov, the question
of K4β has already been addressed. Expanding on this line of inquiry, we
further study this new variant of the generalized Ramsey problem and provide a
conclusively affirmative answer to Alon's question concerning K5β.Comment: Note added: Heath and Zerbib also proved the result on K5β
independently. arXiv:2307.0131