Planar kernel and grundy with d≤3, dout≤2, din≤2 are NP-complete

Uniform Planar Embedding Is Np - Complete

Planar Metric Dimension is NP-complete

We show that Metric Dimension on planar graphs is NP-complete.

Spiral Galaxies Puzzles are NP-complete

We will show that the question of whether or not a given Spiral Galaxies puzzle has a solution is NP-complete. To do so, we construct Spiral Galaxies puzzles which correspond to arbitrary Boolean circuits. A circuit will be satisfied, (that is, have a set of inputs which give the desired outputs) if and only if the corresponding puzzle has a solution. Since Satisfiability is the canonical NP-co...

Selected Slither Link Variants are NP-complete

In a Slither Link puzzle, the player must draw a cycle in a planar graph, such that the number of edges incident to a set of clue faces equals the set of given clue values. We show that for a number of commonly played graph classes, the Slither Link puzzle is NP-complete.

Collapsing cliques to get a planar graph is NP-complete

A graph is a (planar, Kh)-graph if a collection of disjoint clusters can be identified such that the subgraph induced by each cluster is an h-clique and collapsing all clusters yields a planar graph. Recognizing (planar, Kh)-graphs is a special instance of the more general problem of recognizing (X ,Y)-graphs, where X and Y are two chosen families of graphs. This model, together with the (X ,Y)...