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- Jochen Harant, Michael A. Henning
- 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)

- Jochen Harant
- Discussiones Mathematicae Graph Theory
- 2000

For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the independenceâ€¦ (More)

- Jochen Harant, Stanislav Jendrol
- 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)

- Jochen Harant, Anja Pruchnewski, Margit Voigt
- 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)

- Jochen Harant
- Discrete Applied Mathematics
- 2011

We prove a new lower bound on the independence number of a simple connected graph in terms of its degrees.

- Jochen Harant, Dieter Rautenbach
- 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)

- Jochen Harant
- 1999

The well-known greedy algorithm MIN for nding a maximal independent set in a graph G is based on recursively removing the closed neighborhood of a vertex which has (in the currently existing graph)â€¦ (More)

- Jochen Harant, Dieter Rautenbach
- 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)

- Igor Fabrici, Jochen Harant, Stanislav Jendrol
- 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)

- Thomas BÃ¶hme, Jochen Harant, Michal TkÃ¡c
- Journal of Graph Theory
- 1999

We prove the result stated in the title. Furthermore, it is proved that for any " > 0 there is a 1-tough chordal planar graph G " such that the length of a longest cycles of G " is less than "jV (Gâ€¦ (More)