| Naslov: | On b-acyclic chromatic number of a graph |
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| Avtorji: | ID Anholcer, Marcin (Avtor)
ID Cichacz, Sylwia (Avtor)
ID Peterin, Iztok (Avtor) |
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| Datoteke: |  On_b-acyclic_chromatic_number_of-Anholcer-2023.pdf (585,63 KB)
MD5: ECBC67CC810AB4E1174D19FCE152D5C7
 https://link.springer.com/article/10.1007/s40314-022-02156-y
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FERI - Fakulteta za elektrotehniko, računalništvo in informatiko
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| Opis: | Let ▫$G$▫ 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. |
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| Ključne besede: | acyclic b-chromatic number, acyclic coloring, b-coloring |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 14.07.2022 |
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| Datum sprejetja članka: | 07.12.2022 |
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| Datum objave: | 26.12.2022 |
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| Založnik: | Springer (Sociedade Brasileira de Matemática Aplicada e Computacional) |
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| Leto izida: | 2023 |
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| Št. strani: | 20 str. |
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| Številčenje: | Vol. 42, iss. 1, art. 21 |
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| PID: | 20.500.12556/DKUM-84871  |
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| UDK: | 519.17 |
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| COBISS.SI-ID: | 135453955 |
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| DOI: | 10.1007/s40314-022-02156-y |
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| ISSN pri članku: | 2238-3603 |
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| Datum objave v DKUM: | 02.08.2023 |
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| Število ogledov: | 547 |
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| Število prenosov: | 29 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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