Matching theory and generalisations of Hall's theorem

Prerequisites: MAT220, MAT221.

Description: Hall's theorem for when a bipartite graph has a complete matching is continued and generalised in a variety of directions. This project consists of examining the literature and giving an overview of the different directions this is generalised in. Such directions can be: i) partial transversals and transversals of matroids, ii) matchings of graphs in general, iii) matching complexes, and iv) the matching defect polynomial for graphs.

References:

[1] G.Agnarsson, R.Greenlaw Graph theory, modeling, applications and algorithms, Pearson Education, 2007.
[2] J.Oxley, Matroid Theory, Oxford Science Publications, 1992.