Words fixing the kernel network and maximum independent sets in graphs
Description
Abstract: The simple greedy algorithm to find a maximal independent set of a graph can be viewed as a sequential update of a Boolean network, where the update function at each vertex is the conjunction of all the negated variables in its neighbourhood. In general, the convergence of the so-called kernel network is complex. A word (sequence of vertices) fixes the kernel network if applying the updates sequentially according to that word always leads to a fixed point whatever the initial configuration. We prove that determining whether a word fixes the kernel network is coNP-complete. We also consider the so-called permis, which are permutation words that fix the kernel network. We exhibit large classes of graphs that have a permis, but we also construct many graphs without a permis.
Files
paper_3.pdf
Files
(606.7 kB)
Name | Size | Download all |
---|---|---|
md5:b801fb1ebd2458061fc7e288186bc531
|
606.7 kB | Preview Download |
Additional details
Related works
- Is part of
- 10.5281/zenodo.8275851 (DOI)