Cycle Lengths Modulo k in Large 3-connected Cubic Graphs, Advances in Combinatorics

Kasper Szabo Lyngsie, Martin Merker

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Abstract

We prove that for all natural numbers m and k where k is odd, there exists a natural number N(k) such that any 3-connected cubic graph with at least N(k) vertices contains a cycle of length m modulo k. We also construct a family of graphs showing that this is not true for 2-connected cubic graphs if m and k are divisible by 3 and k≥12.
Original languageEnglish
JournalAdvances in Combinatorics
Number of pages36
ISSN2517-5599
DOIs
Publication statusPublished - 2021

Keywords

  • 3-connected
  • Cubic graphs
  • Cycles

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