7,171 research outputs found
Complexity issues on bounded restrictive H-coloring
AbstractWe consider a bounded version of the restrictive and the restrictive list H-coloring problem in which the number of pre-images of certain vertices of H is taken as parameter. We consider the decision and the counting versions, as well as, further variations of those problems. We provide complexity results identifying the cases when the problems are NP-complete or #P-complete or polynomial time solvable. We conclude stating some open problems
Parameterized (in)approximability of subset problems
We discuss approximability and inapproximability in FPT-time for a large
class of subset problems where a feasible solution is a subset of the input
data and the value of is . The class handled encompasses many
well-known graph, set, or satisfiability problems such as Dominating Set,
Vertex Cover, Set Cover, Independent Set, Feedback Vertex Set, etc. In a first
time, we introduce the notion of intersective approximability that generalizes
the one of safe approximability and show strong parameterized inapproximability
results for many of the subset problems handled. Then, we study approximability
of these problems with respect to the dual parameter where is the
size of the instance and the standard parameter. More precisely, we show
that under such a parameterization, many of these problems, while
W[]-hard, admit parameterized approximation schemata.Comment: 7 page
Reconfiguration in bounded bandwidth and treedepth
We show that several reconfiguration problems known to be PSPACE-complete
remain so even when limited to graphs of bounded bandwidth. The essential step
is noticing the similarity to very limited string rewriting systems, whose
ability to directly simulate Turing Machines is classically known. This
resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show
that a large class of reconfiguration problems becomes tractable on graphs of
bounded treedepth, and that this result is in some sense tight.Comment: 14 page
Grad and classes with bounded expansion I. decompositions
We introduce classes of graphs with bounded expansion as a generalization of
both proper minor closed classes and degree bounded classes. Such classes are
based on a new invariant, the greatest reduced average density (grad) of G with
rank r, grad r(G). For these classes we prove the existence of several
partition results such as the existence of low tree-width and low tree-depth
colorings. This generalizes and simplifies several earlier results (obtained
for minor closed classes)
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