[2208.01470] Extremal numbers of disjoint triangles in $r$-partite graphs
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Discrete Mathematics

arXiv:2208.01470 (cs)
[Submitted on 2 Aug 2022 (v1), last revised 24 May 2023 (this version, v3)]

Title:Extremal numbers of disjoint triangles in $r$-partite graphs

Authors:Junxue Zhang
View PDF
Abstract:For two graphs $G$ and $F$, the extremal number of $F$ in $G$, denoted by {ex}$(G,F)$, is the maximum number of edges in a spanning subgraph of $G$ not containing $F$ as a subgraph. Determining {ex}$(K_n,F)$ for a given graph $F$ is a classical extremal problem in graph theory. In 1962, Erdős determined {ex}$(K_n,kK_3)$, which generalized Mantel's Theorem. On the other hand, in 1974, {Bollobás}, Erdős, and Straus determined {ex}$(K_{n_1,n_2,\dots,n_r},K_t)$, which extended Turán's Theorem to complete multipartite graphs. { In this paper,} we determine {ex}$(K_{n_1,n_2,\dots,n_r},kK_3)$ for $r\ge 4$ and $10k-4\le n_1+4k\le n_2\le n_3\le \cdots \le n_r$.
Subjects: Discrete Mathematics (cs.DM)
Cite as: arXiv:2208.01470 [cs.DM]
  (or arXiv:2208.01470v3 [cs.DM] for this version)
  https://doi.org/10.48550/arXiv.2208.01470

Submission history

From: Junxue Zhang [view email]
[v1] Tue, 2 Aug 2022 14:07:48 UTC (13 KB)
[v2] Wed, 17 May 2023 01:38:32 UTC (135 KB)
[v3] Wed, 24 May 2023 07:47:20 UTC (15 KB)
Full-text links:

Access Paper:

license icon view license
Current browse context:
cs.DM
< prev   |   next >
new | recent | 2022-08
Change to browse by:
cs

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)