A Theorem on Indifference Graphs

  • Kieran Hilmer San Diego State University
  • Rom Pinchasi Technion - IIT, Haifa
  • Vadim Ponomarenko San Diego State University
Keywords: indifference graph; interval graph; intersection graph; numerical monoid; numerical semigroup


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

How to Cite
Hilmer, K., Pinchasi, R., & Ponomarenko, V. (2021). A Theorem on Indifference Graphs. The PUMP Journal of Undergraduate Research, 4, 161-167. Retrieved from https://journals.calstate.edu/pump/article/view/2613