Twin-star hypothesis and cycle-free d-partitions of K_2d ]Twin-star hypothesis and cycle-free d-partitions of K_2d

2024/07/19 by Matthew J. Fyfe, Steven R. Lippold, Fyfe, Matthew J. +5
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Primary 05C70 #Secondary 05E18 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2407.13959

openalex publication_date 2024/07/19 · openalex created_date 2024/09/26 · openalex updated_date 2026/07/28

Abstract

In this paper we study an equivalence relation defined on the set of cycle-free d-partitions of the complete graph K_2d. We discuss a conjecture which states that this equivalence relation has only one equivalence class, and show that the conjecture is equivalent with the so called twin-star hypothesis. We check the conjecture in the case d=4 and disuses how this relates to the determinant-like map det^S2.

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• The confirmation of a conjecture on disjoint cycles in a graph