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PreprintarXiv licencearXiv

On the Turán number for the Cartesian product of an odd cycle and a tree

  • Ya-Hong Chen
  • Yong Lu
  • Quan Sun
  • Qi Wu
  • Long-Tu Yuan
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Abstract

Let T be a fixed tree on at least two vertices. We determine the Turán number and all extremal graphs for the Cartesian product of an odd cycle C2m+1 and T, for every fixed integer m≥1 and all sufficiently large n, in terms of its decomposition family. Every extremal graph is the join of an independent set and an extremal graph for that family. The proof combines the Erdős--Sós theorem with weak stability and progressive induction.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026turán,
  title = {{On the Turán number for the Cartesian product of an odd cycle and a tree}},
  author = {Ya-Hong Chen and Yong Lu and Quan Sun and Qi Wu and Long-Tu Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41286},
  eprint = {2610.41286},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41286},
}
RIS
TY  - UNPB
TI  - On the Turán number for the Cartesian product of an odd cycle and a tree
AU  - Ya-Hong Chen
AU  - Yong Lu
AU  - Quan Sun
AU  - Qi Wu
AU  - Long-Tu Yuan
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41286
UR  - https://arxiv.org/abs/2610.41286
AB  - Let T be a fixed tree on at least two vertices. We determine the Turán number and all extremal graphs for the Cartesian product of an odd cycle C_2m+1 and T, for every fixed integer m≥1 and all sufficiently large n, in terms of its decomposition family. Every extremal graph is the join of an independent set and an extremal graph for that family. The proof combines the Erdős--Sós theorem with weak stability and progressive induction.
ER  -