6 problems

Let $G$ be a simple graph with $n$ vertices and minimum degree $\delta(G)\geq 3$, and suppose that $G$ contains a Hamiltonian cycle. Girao, Kittipassorn, and Narayanan's conjecture…

For a graph $G$, an induced packing of cycles is a collection of cycles with no edge between distinct cycles. For a vertex set $X$, let $B_G(X,1)$ be its closed distance-one neighb…

Let $G$ be a connected bipartite graph with bipartition $(X,Y)$. Suppose … let $h=\left\lfloor\frac{n-k}{2}\right\rfloor$, and assume that $\delta(G)\ge r\ge 1$, where $n\ge 2k+2r$…

Let $G$ be a balanced bipartite graph of order $2n$, with minimum degree $\delta(G)\ge r\ge 1$, where $n\ge 2k+2r$ and $k\in\mathbb{Z}$. Adamus–Adamus conjecture. If … then $G$ cont…

Let $G$ be a finite loopless directed graph, allowing both orientations of an edge, and write $d^+(v)$ and $d^-(v)$ for the outdegree and indegree of a vertex $v$. The graph is Eul…

Let $G$ be an $n$-vertex graph, and write $\delta(G)$ for its minimum degree. A Hamiltonian cycle is a cycle spanning all vertices of $G$. The bounded-defect cycle conjecture. If…