2022/07/26 by S. Y. Chan, Chan, S. Y., Kerri Morgan +3
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2207.13007
openalex publication_date 2022/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cycles have many interesting properties and are widely studied in many disciplines. In some areas, maximising the counts of k-cycles are of particular interest. A natural candidate for the construction method used to maximise the number of subgraphs H in a graph G, is the blow-up method. Take a graph G on n vertices and a pattern graph H on k vertices, such that n≥ k, the blow-up method involves an iterative process of replacing vertices in G with a copy of the k-vertex graph H. In this paper, we apply the blow-up method on the family of cycles. We then present the exact counts of cycles of length 4 for using this blow-up method on cycles and generalised theta graphs.