Data Reduction for Graph Coloring Problems

Bart M. P. Jansen; Stefan Kratsch

doi:10.1016/j.ic.2013.08.005

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arXiv · 1104.4229

Data Reduction for Graph Coloring Problems

Bart M. P. Jansen·Stefan Kratsch

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Abstract

This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink instances of coloring problems, in terms of the chosen parameter. It is well known that deciding 3-colorability is already NP-complete, hence parameterizing by the requested number of colors is not fruitful. Instead, we pick up on a research thread initiated by Cai (DAM, 2003) who studied coloring problems parameterized by the modification distance of the input graph to a graph class on which coloring is polynomial-time solvable; for example parameterizing by the number k of vertex-deletions needed to make the graph chordal. We obtain various upper and lower bounds for kernels of such parameterizations of q-Coloring, complementing Cai's study of the time complexity with respect to these parameters. Our results show that the existence of polynomial kernels for q-Coloring parameterized by the vertex-deletion distance to a graph class F is strongly related to the existence of a function f(q) which bounds the number of vertices which are needed to preserve the NO-answer to an instance of q-List-Coloring on F.

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BibTeX RIS

Bart M. P. Jansen, Stefan Kratsch. 2011-04-21. Data Reduction for Graph Coloring Problems. https://doi.org/10.1016/j.ic.2013.08.005

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