Strong non-principality of positive codegree Tur\'an density

Mathematics > Combinatorics [Submitted on 18 Jun 2026] Title:Strong non-principality of positive codegree Turán density View PDF HTML (experimental)Abstract:The \emph{minimum positive codegree} $\delta^+_{k-1}(G)$ of a $k$-graph $G$ is the minimum, over all $(k-1)$-sets that lie in at least one edge, of the number of edges containing that set. The \emph{positive codegree Turán density} of a $k$-graph family $\mathcal{F}$ is the asymptotically maximum value of $\delta^+_{k-1}(G)/n$ over all $\mathcal{F}$-free $k$-graphs $G$ with $n\to\infty$ vertices. In this note, we establish a strong version of non-principality with respect to this density by proving that for every $k\ge3$ there exist two $k$-graphs $F_1$ and $F_2$ such that $$ 0<\gamma^+(F_1, F_2) < \min\{\gamma^+(F_1), \gamma^+(F_2)\}. $$ References & Citations Loading... 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?) ScienceCast (What is ScienceCast?) Demos 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.