Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintarXiv licencearXiv

On the Turán Number of the Cartesian Product of Two Stars

  • Quan Sun
  • Long-Tu Yuan
Open at sourcePDFDOICite

Abstract

We study the Turán number of the Cartesian product of two stars, a family whose order of magnitude is known. For most pairs of star sizes, we determine the leading coefficient exactly. In the remaining congruence class, we give explicit lower and upper bounds for the coefficient at the leading scale. Our lower bounds use blowups of polarity graphs, and our upper bounds use structural estimates on neighbourhoods.

Related

  1. On the Turán number for the Cartesian product of an odd cycle and a tree
    Ya-Hong Chen, Yong Lu, Quan Sun +2
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Eccentric Connectivity Index of Cartesian product and Strong product of Strongly Connected Digraphs
    Vysakh Chakooth, Prasanth G. Narasimha-Shenoi
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. Efficient and Fast Tensor-Product Multinode Shepard Collocation for Elliptic PDEs on Cartesian Grids
    Anouar El Harrak, Hatim Tayeq, Benaissa Zerroudi
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Turán number of three disjoint cliques of arbitrary sizes
    Alexandr Kostochka, Dadong Peng, Zimu Xiang +1
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. On the Turán number of the expansion of the book
    Xin Cheng, Dániel Gerbner, Hilal Hama Karim
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{sun2026turán,
  title = {{On the Turán Number of the Cartesian Product of Two Stars}},
  author = {Quan Sun and Long-Tu Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39486},
  eprint = {2610.39486},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39486},
}
RIS
TY  - UNPB
TI  - On the Turán Number of the Cartesian Product of Two Stars
AU  - Quan Sun
AU  - Long-Tu Yuan
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39486
UR  - https://arxiv.org/abs/2610.39486
AB  - We study the Turán number of the Cartesian product of two stars, a family whose order of magnitude is known. For most pairs of star sizes, we determine the leading coefficient exactly. In the remaining congruence class, we give explicit lower and upper bounds for the coefficient at the leading scale. Our lower bounds use blowups of polarity graphs, and our upper bounds use structural estimates on neighbourhoods.
ER  -