6 problems

Super-strong conjecture on $F$-irregular graphs. For each integer $n\geqslant 3$, there exist infinitely many $n$-hyper-irregular graphs.

Existence conjecture. For every connected graph $F$ on three or more vertices, there exists an $F$-irregular graph.

Let a link-irregular tournament be a tournament in which the directed links of every pair of distinct vertices are non-isomorphic. Link-irregular tournament conjecture. A link-irre…

Let $G=(V,E)$ be a connected graph, and let $m=|E|$ be its number of edges. An edge-irregulator of $G$ is a set $S\subseteq E$ such that $G-S$ is locally irregular, meaning that ev…

Let $G$ be a nice graph of size $m$, and let ${\rm ML}^{\rm W}(G)$ denote the minimum size of an irregularising walk of $G$. The 3m conjecture for irregularising walks states that…

Let $G$ be a graph with $n$ vertices and $m$ edges. Let $\phi$ denote the graph parameter used in the source, and let $\epsilon$ denote the irregularity measure defined earlier in…