For any graph G, the k-improper chromatic number k (G) is the smallest number of colours used in a colouring of G such that each colour class induces a subgraph of maximum degree ...
A graph G is the k-leaf power of a tree T if its vertices are leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most k. Then T is the k...
Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V (G) (the ground set) the image of V (H) under the isomorphism. We consider...
Background: With the continuously increasing demands on knowledge- and data-management that databases have to meet, ontologies and the theories of granularity they use become more...
The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the o...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...