论具有大度数和大循环的二强图中的哈密顿循环

IF 0.7 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

PATTERN RECOGNITION AND IMAGE ANALYSIS Pub Date : 2024-04-10 DOI:10.1134/s105466182401005x

S. Kh. Darbinyan

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引用次数: 0

摘要

Abstract 在这篇笔记中我们证明：让D是一个阶为\(n\)的二强图，使得它的\(n - 1\) 顶点至少有\(n + k\) 度，剩下的顶点\(z\) 至少有\(n - k - 4,\)度，其中\(k\)是一个非负整数。如果\(D\)包含一个长度至少为\(n - k - 2\) 经过\(z,\)的循环，那么\(D\)就是哈密顿的。这个结果在某种意义上是最好的

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On Hamiltonian Cycles in a 2-Strong Digraphs with Large Degrees and Cycles

Abstract

In this note we prove: let D be a 2-strong digraph of order \(n\) such that its \(n - 1\) vertices have degrees at least \(n + k\) and the remaining vertex \(z\) has degree at least \(n - k - 4,\) where \(k\) is a nonnegative integer. If \(D\) contains a cycle of length at least \(n - k - 2\) passing through \(z,\) then \(D\) is Hamiltonian. This result is best possible in some sense.

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来源期刊

PATTERN RECOGNITION AND IMAGE ANALYSIS Computer Science-Computer Graphics and Computer-Aided Design

CiteScore

1.80

自引率

20.00%

发文量

期刊介绍： The purpose of the journal is to publish high-quality peer-reviewed scientific and technical materials that present the results of fundamental and applied scientific research in the field of image processing, recognition, analysis and understanding, pattern recognition, artificial intelligence, and related fields of theoretical and applied computer science and applied mathematics. The policy of the journal provides for the rapid publication of original scientific articles, analytical reviews, articles of the world''s leading scientists and specialists on the subject of the journal solicited by the editorial board, special thematic issues, proceedings of the world''s leading scientific conferences and seminars, as well as short reports containing new results of fundamental and applied research in the field of mathematical theory and methodology of image analysis, mathematical theory and methodology of image recognition, and mathematical foundations and methodology of artificial intelligence. The journal also publishes articles on the use of the apparatus and methods of the mathematical theory of image analysis and the mathematical theory of image recognition for the development of new information technologies and their supporting software and algorithmic complexes and systems for solving complex and particularly important applied problems. The main scientific areas are the mathematical theory of image analysis and the mathematical theory of pattern recognition. The journal also embraces the problems of analyzing and evaluating poorly formalized, poorly structured, incomplete, contradictory and noisy information, including artificial intelligence, bioinformatics, medical informatics, data mining, big data analysis, machine vision, data representation and modeling, data and knowledge extraction from images, machine learning, forecasting, machine graphics, databases, knowledge bases, medical and technical diagnostics, neural networks, specialized software, specialized computational architectures for information analysis and evaluation, linguistic, psychological, psychophysical, and physiological aspects of image analysis and pattern recognition, applied problems, and related problems. Articles can be submitted either in English or Russian. The English language is preferable. Pattern Recognition and Image Analysis is a hybrid journal that publishes mostly subscription articles that are free of charge for the authors, but also accepts Open Access articles with article processing charges. The journal is one of the top 10 global periodicals on image analysis and pattern recognition and is the only publication on this topic in the Russian Federation, Central and Eastern Europe.