On regular d-handicap tournaments

Authors

Bryan Freyberg, University of Minnesota Duluth
Melissa S. Keranen, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

2023

Department

Department of Mathematical Sciences

Abstract

k-regular d-handicap tournament is an incomplete tournament in which n teams, ranked according to the natural numbers, play exactly k < n − 1 different teams exactly once and the strength of schedule of the ith ranked team is d more than the (i − 1)st ranked team for some d ≥ 1. That is, strength of schedules increase arithmetically by d with strength of team. A d-handicap distance antimagic labeling of a graph (Formula Presented)forms an arithmetic sequence with difference d ≥ 1. A graph G which admits such a labeling is called a d-handicap graph. Constructing a k-regular d-handicap tournament on n teams is equivalent to finding a k-regular d-handicap graph of order n. For d = 1 and n even, the existence has recently been completely settled for all pairs (n, k), and some results are known for d = 2. For d > 2, the only known result is restricted to the case where n is divisible by 2d+2. In this paper, we construct infinite families of d-handicap graphs where the order is not restricted to a power of 2.

Publisher's Statement

©2023. Publisher’s version of record: https://doi.org/10.5614/ejgta.2023.11.1.7

Publication Title

Electronic Journal of Graph Theory and Applications

Recommended Citation

Freyberg, B., & Keranen, M. S. (2023). On regular d-handicap tournaments. Electronic Journal of Graph Theory and Applications, 11(1), 81-96. http://doi.org/10.5614/ejgta.2023.11.1.7
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/17264

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This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

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