The Edmonds-Gallai Decomposition for the k-Piece Packing Problem

The Gallai-Edmonds Decomposition for the k-Piece Packing Problem

Packing of induced stars in a graphbyAlexander

We consider simple undirected graphs. An edge subset A of G is called an induced n{star packing of G if every component of the subgraph G[A] induced by A is a star with at most n edges and is an induced subgraph of G. We consider the problem of nding an induced n{star packing of G that covers the maximum number of vertices. This problem is a natural generalization of the classical matching prob...

Decomposition Theorems for Square-free 2-matchings in Bipartite Graphs

The maximum Ck-free 2-matching problem is a problem of finding a maximum simple 2matching which does not contain cycles of length k or less in undirected graphs. The complexity of the problem varies due to k and the input graph. The case where k = 4 and the graph is bipartite, which is called the maximum square-free 2-matching problem in bipartite graphs, is well-solved. Previous results on thi...

The Path-Packing Structure of Graphs

We prove Edmonds-Gallai type structure theorems for Mader’s edgeand vertex-disjoint paths including also capacitated variants, and state a conjecture generalizing Mader’s minimax theorems on path packings and Cunningham and Geelen’s path-matching theorem.

Generalized D-graphs for nonzero roots of the matching polynomial

Recently, Bauer et al. (J Graph Theory 55(4) (2007), 343–358) introduced a graph operator D(G), called the D-graph of G, which has been useful in investigating the structural aspects of maximal Tutte sets in G with a perfect matching. Among other results, they proved a characterization of maximal Tutte sets in terms of maximal independent sets in the graph D(G) and maximal extreme sets in G. Th...