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arXiv · 2609.08484

Sequence b-colorings in graphs

Marko Jakovac·Michael S. Lang
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Abstract

We introduce and begin the study of sequence b-colorings, a natural generalization of the classical notion of b-colorings introduced by Irving and Manlove in 1999. In a sequence b-coloring, each color class is required to contain a prescribed minimum number of color-dominating vertices (CDVs). We establish several fundamental properties of the associated parameters, prove that every sequence is realizable, and show that the problem of deciding whether a particular graph realizes a particular sequence is NP-complete. We also characterize the sequences realized by cycles, obtain results on regular graphs with prescribed girth, and investigate colorings requiring one additional CDV, including a characterization of connected graphs with chromatic number $3$ for which no such coloring exists.

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Marko Jakovac, Michael S. Lang. 2026-09-08. Sequence b-colorings in graphs. https://arxiv.org/abs/2609.08484

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