Tutte sets in graphs I: Maximal tutte sets and D-graphs

@article{Bauer2007TutteSI,
title={Tutte sets in graphs I: Maximal tutte sets and D-graphs},
author={Douglas Bauer and Hajo Broersma and Aurora Morgana and Edward F. Schmeichel},
journal={Journal of Graph Theory},
year={2007},
volume={55},
pages={343-358}
}

A well-known formula of Tutte and Berge expresses the size of a maximum matching in G in terms of what is usually called the deficiency of G. A subset X of G for which this deficiency is attained is called a Tutte set of G. While much is known about maximum matchings, less is known about the structure of Tutte sets. In this paper, we study the structural aspects of maximal Tutte sets in a graph G. Towards this end, we introduce a related graph D(G). We first show that the maximal Tutte sets in… CONTINUE READING