10 problems

Let $H=(V,E,A)$ be a mixed graph, let $\mathcal{D}(V)$ denote the relevant family of subpartitions, and let $d_A^-(X)$ count arcs entering $X$. Let $k\geq0$ and $d\geq1$ be integer…

Let $CMRM(m,n,c)$ be a chordal $m$-ring mixed graph on vertex set $\mathbb Z_m\times\mathbb Z_n$, with the arcs and chords defined by the source, and let $k$ be an even diameter sa…

Let $CRM(N,c)$ be a chordal ring mixed graph with vertex set $\mathbb Z_N$, directed-cycle arcs $i\mathbin{\rightarrow}i+1$, and chords determined by the odd parameter $c$ as in th…

Mixed-graph threshold orientation conjecture. There is a constant $k>2$ such that every mixed graph with minimum pseudo dicut size at least $k$ has an orientation $E^+$ satisfying

Mixed-graph orientation conjecture. There is a constant $k>2$ such that for every mixed graph $M=(V,E\cup A)$, there is an orientation $E^+$ such that

Let $G\in\mathcal{G}_n^{sc}$ be a self-converse mixed graph, let $W=W(G)$ be its walk-matrix, let $\mathscr{U}_G$ be the associated set of Gaussian rational unitary matrices, and l…

Let $G$ be a self-converse mixed graph of order $n$, with walk-matrix … Here $\mathcal{G}_n^{sc}$ denotes the self-converse mixed graphs of order $n$, and $G$ is DGS when it is det…

Total regularity conjecture. All $(r,z,k;-1)$- and $(r,z,k;+1)$-graphs are totally regular.

Bosák's conjecture. A finite graph $G$ is a mixed Moore graph of degree $d$ and diameter $k$ if and only if either $d=1$ and $G$ is $\vec{C}_{k+1}$, or $d=2$ and $G$ is $C_{k+1}$.

Let $K_{m,n}$ be the complete bipartite graph with positive integers $m$ and $n$. A mixed graph is DHS if it is determined by its Hermitian adjacency spectrum among mixed graphs. F…