Abstract
Publisher Summary This chapter discusses the important operation of matroid union and proves that the matroid union operation yields a matroid if one starts with matroids. There are many ways of proving this result. A route is chosen, which has the merit of displaying, along the way, some of the deepest results in matroid theory (for example, Rado's theorem). However, space considerations have prevented from giving the results the motivation they deserve. The key notion in the development is the idea of a submodular function induced through a bipartite graph. The chapter presents an algorithm for matroid union that is an immediate extension of Edmonds' famous algorithm for matroid partition. It also discusses the structure of the union matroid. This algorithm is used to construct the principal partition of the rank function of a matroid.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
