On the structure of locally outerplanar graphs

Hung Lung Wang, Chun Yu Tseng, Jou Ming Chang

Research output: Contribution to journalArticlepeer-review


For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of "minimal corner pairs". In this paper, we show that a "minimal corner pair" may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.

Original languageEnglish
Pages (from-to)1212-1215
Number of pages4
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number6
Publication statusPublished - 2015 Jun 1
Externally publishedYes


  • Geometric Graphs
  • Locally outerplanar graphs
  • Self-intersecting paths

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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