2012/11/30 by Tony Huynh, Sang-il Oum, Sang‐il Oum +1 · 12 citations
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Bipartite graph #Combinatorics #Discrete mathematics #Eulerian path #Graph #Graph minor #Interconnection Networks and Systems #Line graph #Mathematics #Minor (academic) #Partition (number theory) #Pathwidth #Planar graph #Pure mathematics #Robertson–Seymour theorem #Voltage graph #graph theory and CDMA systems #math.CO #msc:05C45
paper · pdf · doi:10.1016/j.ejc.2017.04.010
published in European Journal of Combinatorics 65, 1-14 (Elsevier BV) · 17 pages, 6 figures; minor revision
openalex created_date 2016/06/24 · arxiv created 2017/04/24 · openalex publication_date 2017/05/31 · arxiv updated 2018/05/16 · openalex updated_date 2026/08/05
An even-cycle decomposition of a graph G is a partition of E(G) into cycles of even length. Evidently, every Eulerian bipartite graph has an even-cycle decomposition. Seymour (1981) proved that every 2-connected loopless Eulerian planar graph with an even number of edges also admits an even-cycle decomposition. Later, Zhang (1994) generalized this to graphs with no K5-minor. Our main theorem gives sufficient conditions for the existence of even-cycle decompositions of graphs in the absence of odd minors. Namely, we prove that every 2-connected loopless Eulerian odd-K4-minor-free graph with an even number of edges has an even-cycle decomposition. This is best possible in the sense that `odd-K4-minor-free' cannot be replaced with `odd-K5-minor-free.' The main technical ingredient is a structural characterization of the class of odd-K4-minor-free graphs, which is due to Lovász, Seymour, Schrijver, and Truemper.