稀疏图类列表h填充的复杂度

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2025-06-20 DOI:10.1016/j.tcs.2025.115425

Tatsuya Gima , Tesshu Hanaka , Yasuaki Kobayashi , Yota Otachi , Tomohito Shirai , Akira Suzuki , Yuma Tamura , Xiao Zhou

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引用次数: 0

摘要

将尽可能多的同H∈H同构的子图打包到一个图中，其中H是图的集合，这个问题已经在文献中得到了很好的研究。对于分别包含至少三个顶点和至少三条边的H，已知顶点不相交和边不相交的版本都是np完全的。在本文中，我们考虑了这些问题的“列表变体”：给定一个图G，一个整数k，以及G同构于某个H∈H的子图集合LH，目标是计算LH中k个顶点不相交或边不相交的子图。我们给出了几个正负结果，重点讨论了稀疏图的类别，如有界度图、平面图和有界树宽图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the complexity of list H-packing for sparse graph classes

The problem of packing as many subgraphs isomorphic to some

H \in H

as possible into a graph, where

H

is a collection of graphs, has been well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for H that contains at least three vertices and at least three edges, respectively. In this paper, we consider “list variants” of these problems: Given a graph G, an integer k, and a collection

L_{H}

of subgraphs of G isomorphic to some

H \in H

, the goal is to compute k subgraphs in

L_{H}

that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.