The subchromatic number of a graph
Discrete Mathematics - Graph colouring and variations
Scheduling with incompatible jobs
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Weighted Node Coloring: When Stable Sets Are Expensive
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Graph Subcolorings: Complexity and Algorithms
SIAM Journal on Discrete Mathematics
Graphs and Hypergraphs
On the complexity of decomposing matrices arising in satellite communication
Operations Research Letters
The maximum saving partition problem
Operations Research Letters
| Hi-index | 0.04 |
Starting from a batch scheduling problem, we consider a weighted subcoloring in a graph G; each node v has a weight w(v); each color class S is a subset of nodes which generates a collection of node disjoint cliques. The weight w(S) is defined as max{w(K)=@?"v"@?"Kw(v)|K@?S}. In the scheduling problem, the completion time is given by @?"i"="1^kw(S"i) where S=(S"1,...,S"k) is a partition of the node set of graph G into color classes as defined above. Properties of such colorings concerning special classes of graphs (line graphs of cacti, block graphs) are stated; complexity and approximability results are presented. The associated decision problem is shown to be NP-complete for bipartite graphs with maximum degree at most 39 and triangle-free planar graphs with maximum degree k for any k=3. Polynomial algorithms are given for graphs with maximum degree two and for the forests with maximum degree k. An (exponential) algorithm based on a simple separation principle is sketched for graphs without triangles.