Graph Algorithms and Applications

The mixture of data in real-life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. This book contains some papers reporting recent achievements regarding graph models, algorithms, and applications to problems in the real world, with some focus on optimization and computational complexity

Transversal Partitioning in Balanced Hypergraphs

A transversal of a hypergraph is a set of vertices meeting all the hyperedges. A k-fold transversal\Omega of a hypergraph is a set of vertices such that every hyperedge has at least k elements of \Omega\Gamma In this paper, we prove that a k-fold transversal of a balanced hypergraph can be expressed as a union of k pairwise disjoint transversals and such partition can be obtained in polynomial time. We give an NC algorithm to partition a k-fold transversal of a totally balanced hypergraph into k pairwise disjoint transversals. As a corollary, we deduce that the domatic partition problem is in polynomial class for chordal graphs with no induced odd trampoline and is in NC-class for strongly chordal graphs