11 problems

Asymptotic coloring conjecture. As $s\rightarrow\infty$,

Liu and Ma's conjecture. Every graph with minimum degree at least $k+1$ contains $k$ admissible cycles.

Conjecture on consecutive cycle lengths. Except when $G$ is $K_{k+1}$, the graph $G$ contains $k$ cycles of consecutive lengths.

Liu–Ma conjecture. $G$ contains $eil k/2$ cycles with consecutive odd lengths.

Let $G$ be an $n$-vertex Hamiltonian graph with minimum degree at least $3$. Concentration and separation conjecture. Both of the following hold: 1. $G$ has $\Omega(\sqrt n)$ cycle…

Let $G$ be an $n$-vertex Hamiltonian graph, and let $\delta(G)$ denote its minimum degree. Verstraëte's conjecture. If … then $G$ has $\Omega(n)$ different cycle lengths. This stre…

Let $f_2(n)$ denote the maximum, over all $n$-vertex 2-connected graphs, of the number of cycle lengths that occur exactly once. The authors' conjecture is … This conjecture assert…

For $k\geq 2$, let $\chi_k$ be the largest chromatic number of a graph that does not contain $k$ cycles of consecutive lengths. Sudakov–Verstraëte's conjecture. For every integer…

Conjecture on consecutive odd cycle lengths. If $G$ is a 2-connected non-bipartite graph with minimum degree at least $k+1$, then $G$ contains $\lceil k/2\rceil$ cycles with consec…

A degree 3-critical graph is a graph on $n$ vertices with $2n-2$ edges and no proper induced subgraph of minimum degree $3$. Cycle-count conjecture. Every degree $3$-critical graph…

Uniform splitting conjecture. For every $\varepsilon>0$,