On computing sets of integers with maximum number of pairs summing to powers of 2

03/06/2023

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by   Max A. Alekseyev, et al.

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We address the problem of finding sets of integers of a given size with maximum number of pairs summing to powers of 2. By fixing particular pairs this problem reduces to finding a labeling of the vertices of a given graph with pairwise distinct integers such that the endpoint labels for each edge sum to a power of 2. We propose an efficient algorithm for this problem, which we use to determine the maximum size of graphs of order n that admit such a labeling for all n≤ 18. We also identify the minimal forbidden subgraphs of order ≤ 11, whose presence prevents graphs from having such a labeling.