| Title: | On b-acyclic chromatic number of a graph |
|---|
| Authors: | ID Anholcer, Marcin (Author)
ID Cichacz, Sylwia (Author)
ID Peterin, Iztok (Author) |
|---|
| Files: |  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
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | acyclic b-chromatic number, acyclic coloring, b-coloring |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Submitted for review: | 14.07.2022 |
|---|
| Article acceptance date: | 07.12.2022 |
|---|
| Publication date: | 26.12.2022 |
|---|
| Publisher: | Springer (Sociedade Brasileira de Matemática Aplicada e Computacional) |
|---|
| Year of publishing: | 2023 |
|---|
| Number of pages: | 20 str. |
|---|
| Numbering: | Vol. 42, iss. 1, art. 21 |
|---|
| PID: | 20.500.12556/DKUM-84871  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 2238-3603 |
|---|
| COBISS.SI-ID: | 135453955 |
|---|
| DOI: | 10.1007/s40314-022-02156-y |
|---|
| Publication date in DKUM: | 02.08.2023 |
|---|
| Views: | 543 |
|---|
| Downloads: | 29 |
|---|
| Metadata: |    |
|---|
| Categories: | Misc.
|
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
