2023/06/26 by Ge, Gennian, Xu, Zixiang, Zhang, Yixuan
#05C15 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.14682
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 Kn by t colors with no copy of given graph H in which every color appears an even number of times. When H=K4, 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 K4 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 K5.