13 problems

Let $K_{m,n}$ be a complete bipartite graph with independent vertex sets $\{a_1,\dots,a_m\}$ and $\{b_1,\dots,b_n\}$. Place $a_i$ at $(i,0)$ on the $x$-axis and $b_j$ at $(0,j)$ on…

Complete bipartite graph ideal degree conjecture. The graph ideal for $G=K_{m,n}$ is generated in degree at most

Let $K_{a,b}$ be a bidirectional complete bipartite graph with all edges of equal weight, where $a>b$. Let $A$ and $B$ be its partite sets, with $|A|=a$ and $|B|=b$. For vertices…

Let $K_{s,t}$ be the complete bipartite graph with part sizes $s$ and $t$, where $s\leq t$, and let $C_k(G)$ denote the $k$-coalition number of a graph $G$. Complete bipartite grap…

Let $K_{m,n}$ be the complete bipartite graph with part sizes $m$ and $n$, and define … Here $\operatorname{cr}(G)$ denotes the minimum number of crossings in a plane drawing of a…

Let $K_{s,t}$ be the complete bipartite graph with parts of sizes $s$ and $t$. Complete bipartite monochromatic $k$-connection conjecture. For $t\ge s\ge k\ge 2$, … and, for…

For positive integers $a$ and $b$ with $a>b$, let $K_{a,b}$ denote the complete bipartite graph with parts of sizes $a$ and $b$, and let $\chi_c^\star$ denote its correspondence pa…

List color threshold conjecture.

Let $K(m,n)$ be the complete bipartite graph with part sizes $m$ and $n$, and let $k$-super graceful have the labeling meaning used in the paper. Complete-bipartite classification…

Let $K_{m,n}$ be the complete bipartite graph with $m\ge n\ge 2$, and let $ub(G)$ denote the unit bar visibility number of a graph $G$. Asymptotic unit bar visibility conjecture. F…

Let $K_{n,m}$ be the complete bipartite graph. Denote its critical edge density by $d_{crit}(K_{n,m})=d(n,m)$ and the best edge density obtained from star decomposition by…

Complete-bipartite majority out-domination conjecture.

Aalipour-Hafshejani et al.'s conjecture. For all $a,b\in\mathbb{N}$, if $|a-b|\geq 2$, then ${\cal K}(a,b)$ is ${\cal D}$-unique; that is, every graph with the same domination poly…