Largest 2-Regular Subgraphs in 3-Regular Graphs

Ilkyoo Choi, Ringi Kim, Alexandr V. Kostochka, Boram Park, Douglas B. West

Research output: Contribution to journalArticlepeer-review


For a graph G, let f2(G) denote the largest number of vertices in a 2-regular subgraph of G. We determine the minimum of f2(G) over 3-regular n-vertex simple graphs G. To do this, we prove that every 3-regular multigraph with exactly c cut-edges has a 2-regular subgraph that omits at most max {0 , ⌊ (c- 1) / 2 ⌈} vertices. More generally, every n-vertex multigraph with maximum degree 3 and m edges has a 2-regular subgraph that omits at most max { 0 , ⌊ (3 n- 2 m+ c- 1) / 2 ⌈ } vertices. These bounds are sharp; we describe the extremal multigraphs.

Original languageEnglish (US)
Pages (from-to)805-813
Number of pages9
JournalGraphs and Combinatorics
Issue number4
StatePublished - Jul 1 2019


  • Cubic graphs
  • Cut-edges
  • Factors in graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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