无环、星形和内射着色：无h图的复杂度图

IF 1.1 3区计算机科学 Q1 BUSINESS, FINANCE

Journal of Computer and System Sciences Pub Date : 2025-05-05 DOI:10.1016/j.jcss.2025.103662

Jan Bok , Nikola Jedličková , Barnaby Martin , Pascal Ochem , Daniël Paulusma , Siani Smith

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引用次数: 0

摘要

如果任意两个颜色类分别诱导出一个森林、星林或顶点和边的不相交并，则一个（适当的）着色是无环、星形或内射的。相应的决策问题有无环着色、星形着色和内射着色。我们给出了H-free图上的无环着色、星形着色和内射着色的几乎完全的复杂性分类（对于每一个问题，我们都有一个开放的情况）。此外，如果颜色k的数量是固定的，也就是说，不是输入的一部分，我们给出了完整的复杂性分类。从我们的研究中可以得出，对于固定的k，这三个问题的表现是一样的，但如果k是输入的一部分，这就不再成立了。为了得到我们的几个结果，我们证明了更强的复杂性结果，特别是涉及图的周长和多图的线形图类。

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Acyclic, star and injective colouring: A complexity picture for H-free graphs

A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. The corresponding decision problems are Acyclic Colouring, Star Colouring and Injective Colouring. We give almost complete complexity classifications for Acyclic Colouring, Star Colouring and Injective Colouring on H-free graphs (for each of the problems, we have one open case). Moreover, we give full complexity classifications if the number of colours k is fixed, that is, not part of the input. From our study it follows that for fixed k, the three problems behave in the same way, but this is no longer true if k is part of the input. To obtain several of our results we prove stronger complexity results that in particular involve the girth of a graph and the class of line graphs of multigraphs.

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来源期刊

Journal of Computer and System Sciences 工程技术-计算机：理论方法

CiteScore

3.70

自引率

0.00%

发文量

审稿时长

68 days

期刊介绍： The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions. Research areas include traditional subjects such as: • Theory of algorithms and computability • Formal languages • Automata theory Contemporary subjects such as: • Complexity theory • Algorithmic Complexity • Parallel & distributed computing • Computer networks • Neural networks • Computational learning theory • Database theory & practice • Computer modeling of complex systems • Security and Privacy.