Design theory
On the facial structure of independence system polyhedra
Mathematics of Operations Research
The subchromatic number of a graph
Discrete Mathematics - Graph colouring and variations
Discrete Mathematics - Graph colouring and variations
On the geometric structure of independence systems
Mathematical Programming: Series A and B
A generalization of antiwebs to independence systems and their canonical facets
Mathematical Programming: Series A and B
On the performance of on-line algorithms for partition problems
Acta Cybernetica
Estimations for the domination number of a graph
Discrete Mathematics
Journal of Combinatorial Theory Series B
Discrete Mathematics - Topics on domination
Finding dominating cliques efficiently, in strongly chordal graphs and undirected path graphs
Discrete Mathematics - Topics on domination
Graph properties and hypergraph colourings
Discrete Mathematics
Interpolation theorems for graphs, hypergraphs and matroids
Discrete Mathematics
Domination number and neighbourhood conditions
Discrete Mathematics
A sequential coloring algorithm for finite sets
Discrete Mathematics
Approximation algorithms
Hereditary systems and greedy-type algorithms
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Graph Theory With Applications
Graph Theory With Applications
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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Given an independence system (E,P), the Minimum Partition Problem (MPP) seeks a partition of E into the least number of independent sets. This notion provides a unifying framework for a number of combinatorial optimisation problems, including various conditional colouring problems for graphs. The smallest integer n such that E can be partitioned into n independent sets is called the P-chromatic number of E. In this article we study MPP and the P-chromatic number with emphasis on connections with a few other well-studied optimisation problems. In particular, we show that the P-chromatic number of E is equal to the domination number of a split graph associated with (E,P). With the help of this connection we give a few upper bounds on the P-chromatic number of E in terms of some basic invariants of (E,P).