Remarks on proper conflict-free degree-choosability of graphs with prescribed degeneracyKashima, Masaki (Avtor) Škrekovski, Riste (Avtor) Xu, Rongxing (Avtor) proper conflict-free coloringlist coloringdegree-choosabilitydegeneracyA proper coloring $\phi$ of $G$ is called a proper conflict-free coloring of $G$ if for every non-isolated vertex $v$ of $G$, there is a color $c$ such that $|\phi^{-1}(c) \cap N_G(v)| = 1$. As an analogy of degree-choosability of graphs, we introduced the notion of proper conflict-free (degree $+k$)-choosability of graphs. For a non-negative integer $k$, a graph $G$ is proper conflict-free (degree $+k$)-choosable if for any list assignment $L$ of $G$ with $|L(v)| \ge d_G(v) + k$ for every vertex $v \in V(G)$, $G$ admits a proper conflict-free coloring $\phi$ such that $\phi(v) \in L(v)$ for every vertex $v \in V(G)$. In this note, we first remark if a graph $G$ is $d$-degenerate, then $G$ is proper conflict-free (degree $+d+1$)-choosable. Furthermore, when $d=1$, we can reduce the number of colors by showing that every tree is proper conflict-free (degree $+1$)-choosable. This motivates us to state a question.20262026-02-03 09:10:03Članek v reviji179008UDK: 519.17ISSN pri članku: 0012-365XDOI: 10.1016/j.disc.2026.115003COBISS_ID: 266959619sl