On light cycles in plane triangulations

Stanislav Jendrol', Tomáš Madaras, Roman Soták, Zsolt Tuza

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class script T sign(5) of plane triangulations of minimum degree 5. It is known that each G ∈ script T sign(5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C4 and C5 in each G ∈ script T sign(5) follows. We prove here that each G ∈ script T sign(5) contains also light cycles C6,C7,C8 and C9 such that every vertex is of degree at most 11, 17,29 and 41, respectively. Moreover, we prove that no cycle Ck with k≥11 is light in the class script T sign(5).

Original languageEnglish
Pages (from-to)453-467
Number of pages15
JournalDiscrete Mathematics
Volume197-198
Publication statusPublished - Feb 28 1999

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Keywords

  • Cycles
  • Light subgraph
  • Planar graph
  • Triangulation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Jendrol', S., Madaras, T., Soták, R., & Tuza, Z. (1999). On light cycles in plane triangulations. Discrete Mathematics, 197-198, 453-467.