因子为三角形的有向图的上升子图分解

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-06-29 DOI:10.7151/dmgt.2306

Andrea D. Austin, Brian C. Wagner

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引用次数: 0

摘要

摘要1987年，Alavi、Boals、Chartrand、Erdõs和Oellermann推测所有图都有升子图分解（ASD）。在之前的一篇论文中，Wagner证明了所有有向完全平衡三元图都有ASD。在本文中，我们将证明可以分解为三角形的有向图的所有方向，其中很大一部分三角形是传递的，都具有ASD。我们还将使用该结果来获得具有3n个部分类的完全多部分图的任何方向的ASD，每个部分类包含2个顶点（aK（2:3n））或4个顶点（a K（4:3n））。

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Ascending Subgraph Decompositions of Oriented Graphs that Factor into Triangles

Abstract In 1987, Alavi, Boals, Chartrand, Erdős, and Oellermann conjectured that all graphs have an ascending subgraph decomposition (ASD). In a previous paper, Wagner showed that all oriented complete balanced tripartite graphs have an ASD. In this paper, we will show that all orientations of an oriented graph that can be factored into triangles with a large portion of the triangles being transitive have an ASD. We will also use the result to obtain an ASD for any orientation of complete multipartite graphs with 3n partite classes each containing 2 vertices (a K(2 : 3n)) or 4 vertices (a K(4 : 3n)).

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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.