Generalized Matching Preclusion in Bipartite Graphs

Authors

Zachary WheelerFollow
Eddie Cheng, Oakland UniversityFollow
Dana FerrantiFollow
Laszlo Liptak, Oakland UniversityFollow
Karthik NatarajFollow

Publication Date

2018

Abstract

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph that has no perfect matchings. For many interconnection networks, the optimal such sets are precisely sets of edges incident to a single vertex. The conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond these, and it is defined as the minimum number of edges whose deletion results in a graph with neither isolated vertices nor perfect matchings. In this paper we generalize this concept to get a hierarchy of stronger matching preclusion properties in bipartite graphs, and completely characterize such properties of complete bipartite graphs and hypercubes.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Wheeler, Zachary; Cheng, Eddie; Ferranti, Dana; Liptak, Laszlo; and Nataraj, Karthik (2018) "Generalized Matching Preclusion in Bipartite Graphs," Theory and Applications of Graphs: Vol. 5: Iss. 1, Article 1.
DOI: 10.20429/tag.2018.050101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss1/1