发表机构
University of Maribor; Institute of Mathematics, Physics and Mechanics; Bradley University（马里博尔大学; 数学、物理与力学研究所; 布拉德利大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入序列 b-染色作为经典 b-染色的推广，要求每类含指定数量颜色支配顶点，证明每个序列可实现、判定问题 NP-完全，并刻画圈、正则图及色数 3 连通图的相关性质。
AI 中文摘要
我们引入并开始研究序列 b-染色，这是 Irving 和 Manlove 于 1999 年提出的经典 b-染色概念的自然推广。在序列 b-染色中，每个颜色类被要求包含指定数量的颜色支配顶点（CDV）。我们建立了相关参数的几个基本性质，证明了每个序列都是可实现的，并表明判定特定图是否实现特定序列的问题是 NP-完全的。我们还刻画了由圈实现的序列，在具有指定围长的正则图上获得了结果，并研究了需要额外一个 CDV 的染色，包括对色数为 3 且不存在此类染色的连通图的刻画。
英文摘要
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.
