A Theorem on Indifference Graphs
Keywords:
indifference graph; interval graph; intersection graph; numerical monoid; numerical semigroup
Abstract
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.
Published
2021-08-16
How to Cite
Hilmer, K., Pinchasi, R., & Ponomarenko, V. (2021). A Theorem on Indifference Graphs. The PUMP Journal of Undergraduate Research, 4, 161-167. https://doi.org/10.46787/pump.v4i0.2613
Section
Articles
Copyright (c) 2021 Kieran Hilmer, Rom Pinchasi, Vadim Ponomarenko
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