Connected subgraphs with small degree sums in 3-connected planar graphs

Hikoe Enomoto, Katsuhiro Ota

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


It is well-known that every planar graph has a vertex of degree at most five. Kotzig proved that every 3-connected planar graph has an edge xy such that deg(x) + deg(y) ≤ 13. In this article, considering a similar problem for the case of three or more vertices that induce a connected subgraph, we show that, for a given positive integer t. every 3-connected planar graph G with |V(G)| ≥ t has a connected subgraph H of order t such that ∑x∈V(H) degG(x) ≤ 8t - 1. As a tool for proving this result, we consider decompositions of 3-connected planar graphs into connected subgraphs of order at least t and at most 2t - 1.

Original languageEnglish
Pages (from-to)191-203
Number of pages13
JournalJournal of Graph Theory
Issue number3
Publication statusPublished - 1999 Mar


  • 3-connected planar graph
  • 3-tree
  • Connected subgraph
  • Degree sum

ASJC Scopus subject areas

  • Geometry and Topology


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