4,054 research outputs found
Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult
We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem
Shortest Reconfiguration of Colorings Under Kempe Changes
International audienc
On small Mixed Pattern Ramsey numbers
We call the minimum order of any complete graph so that for any coloring of
the edges by colors it is impossible to avoid a monochromatic or rainbow
triangle, a Mixed Ramsey number. For any graph with edges colored from the
above set of colors, if we consider the condition of excluding in the
above definition, we produce a \emph{Mixed Pattern Ramsey number}, denoted
. We determine this function in terms of for all colored -cycles
and all colored -cliques. We also find bounds for when is a
monochromatic odd cycles, or a star for sufficiently large . We state
several open questions.Comment: 16 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
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