A Theorem on Indifference Graphs

Authors

  • Kieran Hilmer San Diego State University
  • Rom Pinchasi Technion - IIT, Haifa
  • Vadim Ponomarenko San Diego State University

DOI:

https://doi.org/10.46787/pump.v4i0.2613

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.

Author Biographies

Kieran Hilmer, San Diego State University

undergraduate student

Vadim Ponomarenko, San Diego State University

Professor in the Department of Mathematics and Statistics

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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

Issue

Vol. 4 (2021): PUMP Journal of Undergraduate Research

Section

Articles

License

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.