BibTeX
@MISC{Cai14incompressibilityof,
author = {Leizhen Cai and Yufei Cai},
title = {Incompressibility of H-Free Edge Modification Problems},
year = {2014}
}
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Abstract
Given a fixed graph H, the H-Free Edge Deletion (resp., Completion, Editing) problem asks whether it is possible to delete from (resp., add to, delete from or add to) the input graph at most k edges so that the resulting graph is H-free, i.e., contains no induced subgraph isomorphic to H. These H-free edge modification problems are well known to be fixed-parameter tractable for every xed H. In this paper we study the incompressibility, i.e., nonexistence of polynomial kernels, for these H-free edge modification problems in terms of the structure of H, and completely characterize their nonexistence for H being paths, cycles or 3-connected graphs. We also give a sufficient condition for the nonexistence of polynomial kernels for F-Free Edge Deletion problems, where F is a finite set of forbidden induced subgraphs. As an eective tool, we have introduced an incompressible constraint satis-ability problem Propagational-f Satisfiability to express common propa-gational behaviors of events, and we expect the problem to be useful in studying the nonexistence of polynomial kernels in general.
