2013/09/16 by Klas Markström, Markström, Klas
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1309.3870
openalex publication_date 2013/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a construction which shows that there is an infinite set of cyclically 4-edge connected cubic graphs on n vertices with no cycle longer than c4 n for c4=(12)/(13), and at the same time prove that a certain natural family of cubic graphs cannot be used to lower the shortness coefficient c4 to 0. The graphs we construct are snarks so we get the same upper bound for the shortness coefficient of snarks, and we prove that the constructed graphs have an oddness growing linearly with the number of vertices.