17 problems

Cambie's conjecture. Then

Füredi–Kahn–Seymour conjecture. Then

3-edge-colouring conjecture. Every cubic Cayley graph admits a 3-edge colouring.

Defective Goldberg-Seymour conjecture. Every graph $G$ satisfies

Defective list edge-colouring conjecture. For every graph $G$ and every integer $d$,

Odd-defect list edge-colouring conjecture. For every odd integer $d$ and for every graph $G$,

Let $G$ be a simple graph. Two $k$-edge-colourings are Kempe-equivalent if one can be reached from the other through a series of Kempe changes using colours from $\{1,\ldots,k\}$.…

List Colouring Conjecture. If $G$ is a graph of maximum degree $\Delta$ and $L$ is a list assignment to $E(G)$ such that

Local Vizing's theorem. There is an $L$-edge-colouring of $G$.

Let $G$ be a connected graph with minimum degree $\delta\geq 2$ and maximum degree $\Delta$, and let $\chi'_{\subset}(G)$ denote its inclusion chromatic index, the least number of c…

Let $G$ be a connected graph of order at least three, different from the cycle $C_5$. Write $\chi'_{\sum}(G)$ for its neighbour sum distinguishing index and $\Delta(G)$ for its max…

Let $G$ be a multigraph with maximum degree $\Delta(G)$ and maximum multiplicity $\mu(G)$. A forbidden matching is a matching whose edges have been assigned arbitrary, not necessar…

Let $G$ be a graph, let $k\in\mathbb{Z}^+$, and let $D$ be a $k$-optimal set, meaning a $k$-dependent set maximizing $\phi_k(D)=k|D|-|E(G[D])|$. A subgraph is $k$-edge-chromatic if…

Let $H$ be a hypergraph of $d$-intervals. Let $\chi_e(H)$ denote its edge chromatic number, and let $\Delta$ be the maximum degree of a point on any line. Edge-colouring conjecture…

Zhang–Chen–Li–Yao–Lu–Wang's conjecture. For every graph $G$,

Baril–Togni's conjecture. If $G\neq C_5$, then

Liu–Wang–Zhang's conjecture. If $G\notin\{K_2,C_5\}$, then