On the star b-chromatic number of a graph
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916668566929408 |
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| author | Božović, Dragana Štesl, Daša Mesarič Peterin, Iztok |
| author_facet | Božović, Dragana Štesl, Daša Mesarič Peterin, Iztok |
| contents | A star coloring of a graph $G$ is a proper coloring where vertices of every two color classes induce a forest of stars. A strict partial order is defined on the set of all star colorings of $G$. We introduce the star b-chromatic number $S_b(G)$, analogous to the b-chromatic number, as the maximum number of colors in a minimum element of the mentioned order. We present several combinatorial properties of $S_b(G)$, compute the exact value for $S_b(G)$ for several known families and compare $S_b(G)$ with several invariants naturally connected to $S_b(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the star b-chromatic number of a graph Božović, Dragana Štesl, Daša Mesarič Peterin, Iztok Combinatorics 05C15 G.2.2 A star coloring of a graph $G$ is a proper coloring where vertices of every two color classes induce a forest of stars. A strict partial order is defined on the set of all star colorings of $G$. We introduce the star b-chromatic number $S_b(G)$, analogous to the b-chromatic number, as the maximum number of colors in a minimum element of the mentioned order. We present several combinatorial properties of $S_b(G)$, compute the exact value for $S_b(G)$ for several known families and compare $S_b(G)$ with several invariants naturally connected to $S_b(G)$. |
| title | On the star b-chromatic number of a graph |
| topic | Combinatorics 05C15 G.2.2 |
| url | https://arxiv.org/abs/2504.00553 |