TY  - JOUR
A1  - Beckenbach, Isabel
A1  - Scheidweiler, Robert
T1  - Perfect ƒ-Matchings and ƒ-Factors in Hypergraphs - A Combinatorial Approach
JF  - Discrete Mathematics
N2  - We prove characterizations of the existence of perfect ƒ-matchings in uniform mengerian and perfect hypergraphs. Moreover, we investigate the ƒ-factor problem in balanced hypergraphs. For uniform balanced hypergraphs we prove two existence theorems with purely combinatorial arguments, whereas for non-uniform balanced hypergraphs we show that the ƒ-factor problem is NP-hard.
Y1  - 2016
U6  - http://dx.doi.org/10.1016/j.disc.2017.05.005
SN  - 2192-7782
N1  - Als Volltext auch bei ZIB (Zuse Institute Berlin)
VL  - 240
IS  - 10
SP  - 2499
EP  - 2506
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Koster, Arie
A1  - Scheidweiler, Robert
A1  - Tieves, Martin
T1  - A flow based pruning scheme for enumerative equitable coloring algorithms
JF  - A  flow based pruning scheme for enumerative equitable coloring algorithms
N2  - An equitable graph coloring is a proper vertex coloring of a graph G where the sizes of the color classes differ by at most one. The equitable chromatic number is the smallest number k such that G admits such equitable k-coloring. We focus on enumerative algorithms for the computation of the equitable coloring number and propose a general scheme to derive pruning rules for them: We show how the extendability of a partial coloring into an equitable coloring can be modeled via network flows. Thus, we obtain pruning rules which can be checked via flow algorithms. Computational experiments show that the search tree of enumerative algorithms can be significantly reduced in size by these rules and, in most instances, such naive approach even yields a faster algorithm. Moreover, the stability, i.e., the number of solved instances within a given time limit, is greatly improved.
Since the execution of flow algorithms at each node of a search tree is time consuming, we derive arithmetic pruning rules (generalized Hall-conditions) from the network model. Adding these rules to an enumerative algorithm yields an even larger runtime improvement.
Y1  - 2016
U6  - http://dx.doi.org/10.48550/arXiv.1607.08754
N1  - Lehrstuhl II für Mathematik, RWTH Aachen University
SP  - 1
EP  - 30
ER  - 
TY  - JOUR
A1  - Scheidweiler, Robert
A1  - Triesch, Eberhard
T1  - A note on the duality between matchings and vertex covers in balanced hypergraphs
JF  - Journal of Combinatorial Optimization
N2  - We present a new Min-Max theorem for an optimization problem closely connected to matchings and vertex covers in balanced hypergraphs. The result generalizes Kőnig’s Theorem (Berge and Las Vergnas in Ann N Y Acad Sci 175:32–40, 1970; Fulkerson et al. in Math Progr Study 1:120–132, 1974) and Hall’s Theorem (Conforti et al. in Combinatorica 16:325–329, 1996) for balanced hypergraphs.
KW  - Hall’s Theorem
KW  - Koenig’s Theorem
KW  - Duality
KW  - Balanced hypergraph
KW  - Hypergraph
KW  - Vertex cover
KW  - Matching
Y1  - 2016
U6  - http://dx.doi.org/10.1007/s10878-015-9887-5
SN  - 1573-2886
N1  - Lehrstuhl II für Mathematik RWTH Aachen
VL  - 32
IS  - 2
SP  - 639
EP  - 644
PB  - Springer
CY  - Berlin
ER  -