The Existence of Path-Factor Covered Graphs

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-25 DOI:10.7151/dmgt.2353

Guowei Dai

引用次数: 10

Abstract

Abstract A spanning subgraph H of a graph G is called a P≥k-factor of G if every component of H is isomorphic to a path of order at least k, where k ≥ 2. A graph G is called a P≥k-factor covered graph if there is a P≥k-factor of G covering e for any e ∈ E(G). In this paper, we obtain two special classes of P≥2-factor covered graphs. We also obtain two special classes of P≥3-factor covered graphs. Furthermore, it is shown that these results are all sharp.

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路径因子覆盖图的存在性

图G的生成子图H称为G的P≥k因子，如果H的每个分量同构于至少k阶的路径，其中k≥2。图G被称为P≥k因子覆盖图，如果对于任何e∈e（G）存在G覆盖e的P≥k因素。本文得到了P≥2因子覆盖图的两个特殊类。我们还得到了P≥3因子覆盖图的两个特殊类。此外，研究表明，这些结果都是尖锐的。

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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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.