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The Max-Cut problem seeks to determine the maximal cut size in a given graph.
Instead of labeling individual vertices we label subgraphs which partition the given graph.
We also describe all two-distance tight frames obtained from a given graph.
In this paper, we consider the problem of determining whether a given graph is a maximal planar graph or not.
Thus, the solution is a partition of a given graph into as many IDSC as there are sinks.
These are numbers that determine how many lines or nodes would have to be removed from a given graph to disconnect it.
We present experimental results of applying the strategy to designing heuristics for the problem of constructing a maximum independent set of a given graph.
The possible paths in a given graph were represented with different instruction sets, which were then implemented separately by whiplash machines in a test tube.
For a given graph Γ, a Γ-design on v vertices is simply a Γ-decomposition of the complete graph Kv.
This paper considers the problem of augmenting a given graph by a cheapest possible set of additional edges in order to make the graph edge-biconnected.
Some recent contributions on the following problems are considered: firstly, for each balanced-type condition determining the corresponding spectrum for a given graph Γ; secondly, in case some balanced-type spectra coincide for a given graph Γ, checking if the corresponding classes of balanced-type Γ-designs coincide as well.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com