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arXiv · 2504.00553

On the star b-chromatic number of a graph

Dragana Božović·Daša Mesarič Štesl·Iztok Peterin
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Abstract

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 $S_b(G)$.

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Dragana Božović, Daša Mesarič Štesl, Iztok Peterin. 2025-04-01. On the star b-chromatic number of a graph. https://arxiv.org/abs/2504.00553

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