# Jochen Harant

• Discussiones Mathematicae Graph Theory
• 2005
In a graph G, a vertex dominates itself and its neighbors. A subset S âŠ† V (G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a doubleâ€¦ (More)
• Discrete Mathematics
• 2012
We prove new upper bounds on the Thue chromatic number of an arbitrary graph and on the facial Thue chromatic number of a plane graph in terms of its maximum degree. Â© 2011 Elsevier B.V. All rightsâ€¦ (More)
• Combinatorics, Probability & Computing
• 1999
A k-dominating set is a set D k V such that every vertex i 2 V nD k has at least k i neighbours in D k. The k-domination number k (G) of G is the cardinality of a smallest k-dominating set of G. Forâ€¦ (More)
• Discrete Applied Mathematics
• 2011
We prove that if G = (VG, EG) is a finite, simple, and undirected graph with Îº components and independence number Î±(G), then there exist a positive integer k âˆˆ N and a function f : VG â†’ N0 withâ€¦ (More)
• Discrete Mathematics
• 2009
The domination number Î³(G) of a (finite, undirected and simple) graph G = (V, E) is the minimum cardinality of a set D âŠ† V of vertices such that every vertex in V \ D has a neighbour in D. Thisâ€¦ (More)
• Discussiones Mathematicae Graph Theory
• 2008
The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are: 1. Every 3-connected simple planar graph G that contains a k-path, aâ€¦ (More)