NP-Completeness of the Eulerian Walk Problem for a Multiple Graph

IF 0.6 Q4 AUTOMATION & CONTROL SYSTEMS
A. V. Smirnov
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引用次数: 0

Abstract

In this article, we consider undirected multiple graphs of any natural multiplicity k > 1. A multiple graph contains edges of three types: ordinary edges, multiple edges, and multiedges. Each edge of the last two types is the union of linked edges that connect 2 or (k + 1) vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, then it can be incident to other multiple edges, and it can also be the common end of k linked edges of a multiedge. If a vertex is the common end of a multiedge, then it cannot be the common end of another multiedge. We study the problem of the Eulerian walk (cycle or trail) in a multiple graph, which generalizes the classical problem for an ordinary graph. We prove that the recognition variant of the multiple Eulerian walk problem is NP-complete. To do this, we first prove NP-completeness of the auxiliary problem of covering trails with the given endpoints in an ordinary graph.

Abstract Image

多图欧拉行走问题的 NP 完备性
在本文中,我们考虑任意自然多重k >;1. 一个多重图包含三种类型的边:普通边、多重边和多重边。最后两种类型的每条边都是连接2个或(k + 1)个顶点的连接边的并集。连接边应同时使用。如果一个顶点关联到一条多边,那么它也可以关联到其他多条边,它也可以是一条多边的k条连接边的公共端。如果一个顶点是一条多边的公共端,那么它就不能是另一条多边的公共端。研究了多图中的欧拉行走(循环或轨迹)问题,推广了普通图的经典问题。证明了多重欧拉行走问题的识别变体是np完全的。为了做到这一点,我们首先证明了在普通图中用给定端点覆盖轨迹的辅助问题的np完备性。
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来源期刊
AUTOMATIC CONTROL AND COMPUTER SCIENCES
AUTOMATIC CONTROL AND COMPUTER SCIENCES AUTOMATION & CONTROL SYSTEMS-
CiteScore
1.70
自引率
22.20%
发文量
47
期刊介绍: Automatic Control and Computer Sciences is a peer reviewed journal that publishes articles on• Control systems, cyber-physical system, real-time systems, robotics, smart sensors, embedded intelligence • Network information technologies, information security, statistical methods of data processing, distributed artificial intelligence, complex systems modeling, knowledge representation, processing and management • Signal and image processing, machine learning, machine perception, computer vision
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