7 problems

Simultaneous multipartite subhypergraph conjecture. There exists a partition of $V$ into $r$ classes $V_1,\dots,V_r$ such that, for every $i=1,\dots,\ell$, at least

Dhawan's conjecture. For every $k\geqslant 2$, there is a constant $c=c(k)>0$ such that, for all sufficiently large $\Delta$,

Let $k\geqslant 2$, let $\Delta$ be sufficiently large, and let $H$ be a $k$-partite $k$-graph of maximum degree at most $\Delta$. Write $\chi_\ell(H)$ for the list chromatic numbe…

Let $\mathscr K_{m_1,\ldots,m_n}^{3}$ be the complete multipartite 3-uniform hypergraph whose parts have sizes $m_1,\ldots,m_n$, and let $\lambda \mathscr K_{m_1,\ldots,m_n}^{3}$ d…

Let $r\ge 2$, and let $p_1,p_2,\ldots,p_k$ be positive integers. For each $i$, let $V_i$ be a part of size $p_i$, and let $K_{p_1,p_2,\ldots,p_k}^r$ be the $r$-complete $k$-partite…

Let $H$ be an $n$-balanced $r$-partite $r$-graph, and let $I$ be a subset of $[r]:=\{1,2,\ldots,r\}$. An $I$-tuple is an element of $\times_{i\in I}V_i$, and an $I^c$-tuple is defi…

Let $H$) be an $n$-balanced $r$-partite $r$-graph, and let $I$ be a subset of $[r]:=\{1,2,\ldots,r\}$. An $I$-tuple is an element of $\times_{i\in I}V_i$, and write…