Homology of graph burnings

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-26 DOI:10.1016/j.topol.2025.109486

Yuri Muranov, Anna Muranova

引用次数: 0

Abstract

In this paper we study graph burnings using methods of algebraic topology. We prove that the time function of a burning is a graph map to a path graph. We use this fact to define a category whose objects are graph burnings and morphisms are graph maps which commute with the time functions of the burnings. In this category we study relations between burnings of different graphs and, in particular, between burnings of a graph and its subgraphs. For every graph, we define a simplicial complex, arising from the set of all the burnings, which we call a configuration space of the burnings. The simplicial structure of the configuration space defines burning homology of the graph. We describe properties of the configuration space and the burning homology theory. We prove that the one-dimensional skeleton of the configuration space of a graph G coincides with the complement graph of G. The results are illustrated with numerous examples.

查看原文本刊更多论文

图形燃烧的同源性

本文利用代数拓扑的方法研究了图的燃烧问题。证明了燃烧的时间函数是路径图的图映射。我们用这个事实来定义一个范畴，它的对象是图燃烧，而态射是与燃烧的时间函数交换的图映射。在这个范畴中，我们研究了不同图的燃烧之间的关系，特别是图与其子图的燃烧之间的关系。对于每一个图，我们定义一个由所有燃烧的集合产生的简单复形，我们称之为燃烧的位形空间。构型空间的简单结构定义了图的燃烧同调性。描述了构型空间的性质和燃烧同调理论。证明了图G的构形空间的一维骨架与G的补图重合，并给出了大量实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.