Applications of the Bergelson–Leibman and the Mordell–Faltings Theorems

Alexander Soifer
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Alexander Soifer: University of Colorado at Colorado Springs, College of Letters, Arts, and Sciences

Chapter Chapter 49 in The New Mathematical Coloring Book, 2024, pp 647-650 from Springer

Abstract: Abstract To achieve a girth 12 unit-distance graph, Paul O’Donnell alters the set D of allowable constant differences. This changes which sets are in S (i.e., which sets of the foundation vertices get odd cycles attached). It is no longer enough for the sets in S to have intersection of size at most one, as we required in Chap. 48 . In addition, O’Donnell requires now that no three sets in S intersect pairwise. How does one achieve this?

Date: 2024
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DOI: 10.1007/978-1-0716-3597-1_49

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