Arc index of spatial graphs

Min Jung Lee, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review


Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index α(G) of any spatial graph G as α(G) ≤ c(G) + e + b where c (G) is the minimal crossing number of G, e is the number of edges, and b is the number of bouquet cut-components. This upper bound is lowest possible.

Original languageEnglish
Pages (from-to)406-415
Number of pages10
JournalJournal of Graph Theory
Issue number3
Publication statusPublished - 2019 Mar


  • arc index
  • spatial graph
  • upper bound

ASJC Scopus subject areas

  • Geometry and Topology


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