Gaps in the cycle spectrum of 3-connected cubic planar graphs

Martin Merker

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We prove that, for every natural number k , every sufficiently large 3-connected cubic planar graph has a cycle whose length is in [k,2k+9] . We also show that this bound is close to being optimal by constructing, for every even k≥4 , an infinite family of 3-connected cubic planar graphs that contain no cycle whose length is in [k,2k+1]
Original languageEnglish
JournalJournal of Combinatorial Theory. Series B
Volume146
Pages (from-to)68-75
ISSN0095-8956
DOIs
Publication statusPublished - 2021

Keywords

  • Cycles
  • Cycle spectrum
  • 3-connected
  • Cubic
  • Planar graphs

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