Dömötör Pálvölgyi

Indecomposable Coverings with Concave Polygons

We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold covering of some point set by the translates of this polygon that cannot be decomposed into two coverings. Moreover, we give a complete classification of open polygons with this property. We also construct for any polytope (having dimension at least three) and for any k, a k-fold covering of the space by its translates that cannot be decomposed into two coverings.

Drawing Planar Graphs of Bounded Degree with Few Slopes

We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function

Convex Polygons are Cover-Decomposable

f

Bin packing via discrepancy of permutations

with the property that every planar graph

Forbidden Hypermatrices Imply General Bounds on Induced Forbidden Subposet Problems

G

Octants Are Cover-Decomposable

with maximum degree

Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs

d

Octants are cover-decomposable into many coverings

admits a drawing with noncrossing straight-line edges, using at most

Survey on Decomposition of Multiple Coverings

f(d)

Drawing planar graphs of bounded degree with few slopes

different slopes. If we allow the edges to be represented by polygonal paths with one bend, then