Z -transformation graphs of perfect matchings of hexagonal systems
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It is proved that Z ( H ) is a connected bipartite graph if H has at least one perfect matching and that those hexagonal systems whose Z -transformation graphs are not 2-connected are given.About:
This article is published in Discrete Mathematics.The article was published on 1988-12-01 and is currently open access. It has received 86 citations till now. The article focuses on the topics: Claw-free graph & Factor-critical graph.read more
Citations
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Book ChapterDOI
Feedback set problems
TL;DR: Dramatic progress has occurred in developing approximation algorithms with provable performance; new bounds have been established one after the other and it is probably fair to say that feedback set problems are becoming among the most exciting frontend problems in combinatorial optimization.
Journal ArticleDOI
Plane elementary bipartite graphs
Heping Zhang,Fuji Zhang +1 more
TL;DR: Various properties of plane elementary bipartite graphs are studied so that many important results previously obtained for hexagonal systems are treated in a unified way.
Feedback Set Problems.
TL;DR: This paper is a short survey of feedback set problems and aims to provide a baseline for future research on how to deal with these problems more effectively.
Journal ArticleDOI
Forcing matchings on square grids
Lior Pachter,Peter S. Kim +1 more
TL;DR: It is shown that for the 2n × 2n square grid, the forcing number of any perfect matching is bounded below by n and above by n^2, which establishes a connection between the forcing problem and the minimum feedback set problem.
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Hexagonal systems with forcing edges
Fuji Zhang,Xueliang Li +1 more
TL;DR: Using the concept of Z-transformation of hexagonal system, a characterization is given for the hexagonal systems with forcing edges and all forcing edges is such systems and the generating function is determined.
References
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Book
Introduction to the theory of benzenoid hydrocarbons
Ivan Gutman,Sven J. Cyvin +1 more
TL;DR: In this article, the authors proposed a method for the enumeration of Kekule structures and derived a set of properties of Benzenoid Hydrocarbons, including symmetry, symmetry, vertices, edges, and edges.
Journal ArticleDOI
Matroid basis graphs. II
TL;DR: In this article, the problem of characterizing regular and graphic matroids through their basis graphs is discussed, and many results are obtained quite easily with the aid of certain pseudo-combivalence systems of 0-1 matrices.
Journal ArticleDOI
Perfect matchings in hexagonal systems
TL;DR: A simple algorithm is developed which allows to decide whether or not a given hexagonal system has a perfect matching (and to find such a matching).