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PreprintarXiv licencearXiv

Local Ore Conditions for Rainbow Pancyclicity and Vertex-Pancyclicity in Graph Systems

  • Ailian Chen
  • Jiahuang Lin
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Abstract

We investigate rainbow pancyclicity and vertex-pancyclicity of graph systems satisfying a local Ore-type degree condition. All graphs in the system share the same vertex set. We prove that if each graph is 2-connected and satisfies our local Ore condition, then the graph system is either rainbow pancyclic and vertex-pancyclic for cycles of length from 4 to n, or all graphs are identical balanced complete bipartite graphs on an even vertex set. A stronger degree threshold ensures full rainbow vertex-pancyclicity. All thresholds we obtain are tight. Our proofs rely on cycle extension techniques and neighborhood separation arguments.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026local,
  title = {{Local Ore Conditions for Rainbow Pancyclicity and Vertex-Pancyclicity in Graph Systems}},
  author = {Ailian Chen and Jiahuang Lin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24427},
  eprint = {2610.24427},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24427},
}
RIS
TY  - UNPB
TI  - Local Ore Conditions for Rainbow Pancyclicity and Vertex-Pancyclicity in Graph Systems
AU  - Ailian Chen
AU  - Jiahuang Lin
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24427
UR  - https://arxiv.org/abs/2610.24427
AB  - We investigate rainbow pancyclicity and vertex-pancyclicity of graph systems satisfying a local Ore-type degree condition. All graphs in the system share the same vertex set. We prove that if each graph is 2-connected and satisfies our local Ore condition, then the graph system is either rainbow pancyclic and vertex-pancyclic for cycles of length from 4 to n, or all graphs are identical balanced complete bipartite graphs on an even vertex set. A stronger degree threshold ensures full rainbow vertex-pancyclicity. All thresholds we obtain are tight. Our proofs rely on cycle extension techniques and neighborhood separation arguments.
ER  -