子矩阵超图的完全着色

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-12-01 DOI:10.1134/S1990478924030050

S. O. Borodin, A. A. Taranenko

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引用次数: 0

摘要

子矩阵超图\( G_{n\times m} \)是一个超图，其顶点是\( n\times m \)矩阵的条目，超边是\( 2 \)阶的子矩阵。本文考虑了子矩阵超图的完全着色，并研究了它们的参数。给出了\( G_{n\times m} \)的完美着色的几个构造，并证明了\( 2 \) -设计的关联矩阵是子矩阵超图的完美着色。此外，我们还描述了超图\( G_{2\times m} \)和\( G_{3\times m} \)的所有完美2-着色。

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Perfect Colorings of Submatrix Hypergraphs

A submatrix hypergraph \( G_{n\times m} \) is a hypergraph whose vertices are entries of an \( n\times m \) matrix and hyperedges are submatrices of order \( 2 \). In this paper, we consider perfect colorings of submatrix hypergraphs and study their parameters. We provide several constructions of perfect colorings of \( G_{n\times m} \) and prove that the incidence matrices of \( 2 \)-designs are perfect colorings of the submatrix hypergraph. Moreover, we describe all perfect 2-colorings of hypergraphs \( G_{2\times m} \) and \( G_{3\times m} \).

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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.