Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles

2015/01/28 by Francesca Merola, Merola, Francesca, Tommaso Traetta +1
Computer Science · Engineering · Mathematics · #05C70 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Mathematics and Applications #graph theory and CDMA systems #math.CO #msc:05C70

paper · pdf · doi:10.48550/arxiv.1501.06999

31 pages

openalex publication_date 2015/01/28 · arxiv created 2016/03/31 · arxiv updated 2016/04/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

It is conjectured that for every pair (ℓ,m) of odd integers greater than 2 with m ≡ 1 \pmodℓ, there exists a cyclic two-factorization of K_{ℓ m} having exactly (m-1)/2 factors of type ℓ^m and all the others of type m^ℓ. The authors prove the conjecture in the affirmative when ℓ ≡ 1 \pmod4 and m ≥ ℓ² -ℓ + 1.

Citations

• A Dynamic Survey of Graph Labeling

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