A Theorem on Indifference Graphs
An indifference graph P has as vertices a set of points on the real line, with an edge between every two points at most 1 apart. For every point x in P, we set N(x) to be the set of points that are adjacent to x. Fix an indifference graph P, and a positive integer k. Suppose that for every x in P, k divides |N(x)|. We show that the number of points in P is also divisible by k.
Copyright (c) 2021 Kieran Hilmer, Rom Pinchasi, Vadim Ponomarenko
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