On b-acyclic chromatic number of a graphAnholcer, Marcin (Avtor) Cichacz, Sylwia (Avtor) Peterin, Iztok (Avtor) acyclic b-chromatic numberacyclic coloringb-coloringLet ▫$G$▫ be a graph. We introduce the acyclic b-chromatic number of ▫$G$▫ as an analog to the b-chromatic number of ▫$G$▫. An acyclic coloring of a graph ▫$G$▫ is a map ▫$c:V(G)\rightarrow \{1,\dots,k\}$▫ such that ▫$c(u)\neq c(v)$▫ for any ▫$uv\in E(G)$▫ and the induced subgraph on vertices of any two colors ▫$i,j\in \{1,\dots,k\}$▫ induce a forest. On a set of all acyclic colorings of a graph ▫$G$▫ we define a relation whose transitive closure is a strict partial order. The minimum cardinality of its minimal element is then the acyclic chromatic number ▫$A(G)$▫ of ▫$G$▫ and the maximum cardinality of its minimal element is the acyclic b-chromatic number ▫$A_b(G)$▫ of ▫$G$▫. We present several properties of ▫$A_b(G)$▫. In particular, we derive ▫$A_b(G)$▫ for several known graph families, derive some bounds for ▫$A_b(G)$▫, compare ▫$A_b(G)$▫ with some other parameters and generalize some influential tools from b-colorings to acyclic b-colorings.Springer (Sociedade Brasileira de Matemática Aplicada e Computacional)20232023-08-02 10:54:48Članek v reviji84871UDK: 519.17COBISS_ID: 135453955DOI: 10.1007/s40314-022-02156-yISSN pri članku: 2238-3603sl