Total Domination in Graphs with Large Minimum Degree

• Applicant: Dr. Christian Löwenstein
• Subject Area: Mathematics
• Term: from 2011 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 193324949

A graph G=(V,E) is a finite set V of elements, called vertices, together with a finite set E of 2-element subsets of V, called edges. The degree of a vertex v in a graph G is the number of edges of G that contain v. The smallest degree of all vertices of a graph G is the minimum degree of G. A total dominating set in a graph G=(V,E) is a subset S of V, such that every vertex v belongs to at least one edge that contains at least one vertex different from v in S. The total domination number of G is the smallest order of a total dominating set of G. During my funding period I wish to prove upper bounds on the total domination number of graphs with large minimum degree.

• DFG Programme: Research Fellowships
• International Connection: South Africa
• Host: Professor Dr. Michael A. Henning