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- Arnfried Kemnitz, Jens-Peter Bode, Andrea Hackmann, Rebecca Klages
- 2002

Given positive integers k and d with k ≥ 2d, a (k, d)-total coloring of a simple and finite graph G is an assignment c of colors {0, 1,. .. , k − 1} to the vertices and edges of G such that d ≤ |c(x) − c(x ′)| ≤ k − d whenever x and x ′ are two adjacent edges, two adjacent vertices or an edge incident to a vertex. The circular total chromatic number χ ′′ c… (More)

- ARNFRIED KEMNITZ
- 2007

- Arnfried Kemnitz, Heiko Harborth
- Discrete Mathematics
- 2001

A plane integral drawing of a planar graph G is a realization of G in the plane such that the vertices of G are mapped into distinct points and the edges of G are mapped into straight line segments of integer length which connect the corresponding vertices such that two edges have no inner point in common. We conjecture that plane integral drawings exist… (More)

- Arnfried Kemnitz, Halka Kolberg
- Discrete Mathematics
- 1998

An integer distance graph is a graph G(D) with the set of integers as vertex set and with an edge joining two vertices u and v if and only if ju ? vj 2 D where D is a subset of the positive integers. We determine the chromatic number (D) of G(D) for some nite distance sets D such as sets of consecutive integers and special sets of cardinality 4.

- Arnfried Kemnitz, Ingo Schiermeyer
- Discussiones Mathematicae Graph Theory
- 2011

An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that rc(G) = 2 for every connected graph G of order n… (More)

- Heiko Harborth, Arnfried Kemnitz, Meinhard Möller
- Discrete & Computational Geometry
- 1993

- Arnfried Kemnitz, Massimiliano Marangio
- Discrete Mathematics
- 2001

An integer distance graph is a graph G(D) with the set of integers as vertex set and with an edge joining two vertices u and v if and only if ju ? vj 2 D where D is a subset of the positive integers. We determine the chromatic number (D) of G(D) if D is a 4-element set of the form

- Maria Axenovich, Heiko Harborth, Arnfried Kemnitz, Meinhard Möller, Ingo Schiermeyer
- Graphs and Combinatorics
- 2007

Let Q n be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f (G, H) be the largest number of colors such that there exists an edge coloring… (More)

- ARNFRIED KEMNITZ
- 2003

A (k; d)-coloring (k; d 2 IN; k 2d) is an assignment c of colors f0; 1; : : : ; k ?1g to the vertices of G such that d jc(v 1) ? c(v 2)j k ? d whenever two vertices v 1 ; v 2 are adjacent. The circular chromatic number c (G) is deened by c (G) = inffk=d : G admits a (k; d)?coloringg. We determine c (G) for Platonic solid graphs, Archimedean solid graphs,… (More)

- Arnfried Kemnitz, Massimiliano Marangio
- Discrete Mathematics
- 2007