Off-Diagonal Ramsey Multiplicity

2023/06/30 by Moss, Elena, Noel, Jonathan A. · 1 citation
#05C35 #05D10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.17388

Abstract

The Ramsey multiplicity problem asks for the minimum asymptotic density of monochromatic labelled copies of a graph H in a red/blue colouring of the edges of K_n. We introduce an off-diagonal generalization in which the goal is to minimize a certain weighted sum of the densities of red copies of one graph and blue copies of another. We build up various properties of this new notion, including a useful "dual formulation," and use these results to solve the problem for several pairs of graphs.

Cited by

• Ramsey multiplicity for ordered graphs

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