使用同调路径的Hypergraph边表示

IF 0.58 Q3 Engineering Journal of Applied and Industrial Mathematics Pub Date : 2023-11-04 DOI:10.1134/S1990478923030201

M. N. Vyalyi, V. E. Karpov

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引用次数: 0

摘要

我们考虑了超图在图上的实现问题，前提是每个超图都是由恰好两个顶点具有奇数度的子图实现的。这个问题与循环双覆盖猜想有关。我们证明了检验实现的存在性在计算上是困难的。硬度在各种设置中得到证明：对于在所有图上、在简单图上以及在来自几个受限类的图上的实现。

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Hypergraph Edge Representations with the Use of Homological Paths

We consider the problem of realization of hypergraphs on a graph provided each hyperedge is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to Cycle Double Cover conjecture. We prove that checking the existence of realization is computationally hard. The hardness is proved in various settings: for realizations on all graphs, on simple graphs, and on graphs from several restricted classes.

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.