James Oxley
- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198566946
- eISBN:
- 9780191774904
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566946.003.0012
- Subject:
- Mathematics, Educational Mathematics
This chapter considers several more matroid constructions. The chapter is organized as follows. Section 11.2 considers several applications of submodular functions, one of which is in the proof of ...
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This chapter considers several more matroid constructions. The chapter is organized as follows. Section 11.2 considers several applications of submodular functions, one of which is in the proof of Hall's Marriage Theorem, a result that specifies precisely when a family of sets has a transversal. Section 11.3 discusses the operation of matroid union and presents several of its attractive applications. Section 11.4 considers the problem of sticking two matroids together across a common restriction. Much of the discussion there focuses on a generalization of the operation of parallel connection. The last operation is used in Section 11.5 to define a matroid generalization of the graph operation of Δ-Y exchange.Less
This chapter considers several more matroid constructions. The chapter is organized as follows. Section 11.2 considers several applications of submodular functions, one of which is in the proof of Hall's Marriage Theorem, a result that specifies precisely when a family of sets has a transversal. Section 11.3 discusses the operation of matroid union and presents several of its attractive applications. Section 11.4 considers the problem of sticking two matroids together across a common restriction. Much of the discussion there focuses on a generalization of the operation of parallel connection. The last operation is used in Section 11.5 to define a matroid generalization of the graph operation of Δ-Y exchange.
