Kernelization Upper Bounds for Parameterized Graph Coloring Problems
Year: 2013
Type: dissertation
Abstract: This thesis studies the kernelization complexity of graph coloring problems\nwith respect to certain structural parameterizations of the input instances, fol-\nlowing up on a paper by Jansen and Kratsch (FCT, 2011). In their paper they\nstudy how well polynomial-time data reductions can provably shrink instances\nof coloring problems, in terms of the chosen parameter. In this thesis we do the\nsame except we use different parameters on slightly harder coloring problems.\nThe paper by Jansen and Kratsch shows some interesting results about coloring\nproblems parameterized by the modification distance of the input graph to a\ngraph class on which coloring is polynomial-time solvable, for example parame-\nterizing by the number k of vertex-deletions needed to make the graph chordal.\nIn this thesis we obtain results on parameterizations of Chromatic Number.\nEvery parameterization in this thesis is either by the number k of edge-deletions,\nedge-additions or edge-modifications (edge-deletions and edge-additions) needed\nto transform the input graph into a graph which is a member of a well known\ngraph class, e.g. a forest. We obtain various upper and lower bounds for kernels\nof such parameterizations of Chromatic Number.
Author: P. de Weijer
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W112717413