10 problems

Kühn–Osthus conjecture. Every regular tripartite tournament has a Hamilton decomposition.

Let $G$ be an $n \times n \times n$ tripartite graph, and let $\delta(G)$ denote its minimum degree. For an integer $t\geqslant 2$, let $\tau$ be the additive term in the condition…

Let $R=\{(\alpha,\beta,\gamma)\in[0,1]^3:\alpha\beta+\gamma>1,\alpha\gamma+\beta>1,\beta\gamma+\alpha>1\}$, and let … Define…

Let $k\geq 2$ and let $n$ be sufficiently large. For $1\geq\alpha,\beta,\gamma\geq 0$, an $(k,n)$-cyclic triple is a triple satisfying the six cyclic density inequalities stated in…

Let $t\leqslant s\leqslant r$ and let $G$ be an $n\times n\times n$ tripartite graph. Write $\tau(n)$ for the least additive term such that every such graph with minimum degree at…

Bollobás–Erdős–Szemerédi conjecture. There is a constant $c>0$ such that

Let $ell$, $m$, and $p$ be positive integers such that $ellge mp$. Let $K{n1,n2,n3}$ be a complete tripartite host graph with $n1ge n2ge n3$, where $n3$ is sufficiently large com…

Let $\alpha,\beta,\gamma\in[0,1]$, let $R_2\subseteq[0,1]^3$ be the second region defined in the paper, and let $H_9$ be the specified tripartite graph. For a weighting $w$,…

Let $\alpha,\beta,\gamma\in[0,1]$ be edge densities of a weighted tripartite graph, let $R\subseteq[0,1]^3$ be the region defined in the paper, let $R_2=R\setminus R_1$, and let…

Let $\alpha,\beta,\gamma\in[0,1]$ be the prescribed edge densities, let $T_{\min}(\alpha,\beta,\gamma)$ denote the minimum triangle density over weighted tripartite graphs with the…