This paper investigates ultrafilters in the context of connectivity systems, defined as pairs (X,
f) where X is a finite set and f is a symmetric submodular function. Ultrafilters, essential in …

Stack-number is not bounded by queue-number Page 1 COMBINATORICA Bolyai Society –
Springer-Verlag 0209–9683/122/$6.00 c 2022 János Bolyai Mathematical Society and …

The crossing number is a popular tool in graph drawing and visualization, but there is not
really just one crossing number; there is a large family of crossing number notions of which …

In a total order of the vertices of a graph, two edges with no endpoint in common can
be\emphcrossing,\emphnested, or\emphdisjoint. A\emphk-stack (respectively,\emphk …

Given a finite, undirected, simple graph G, we are concerned with operations on G that
transform it into a planar graph. We give a survey of results about such operations and …

Around 1958, Hill described how to draw the complete graph K_n K n with Z (n):= 1 4\Big ⌊
n 2\Big ⌋\Big ⌊ n-1 2\Big ⌋\Big ⌊ n-2 2\Big ⌋\Big ⌊ n-3 2\Big ⌋ Z (n):= 1 4⌊ n 2⌋⌊ n− 1 …

We prove that the stack-number of the strong product of three n-vertex paths is Θ (n 1/3). The
best previously known upper bound was O (n). No non-trivial lower bound was known. This …

This paper deals with the characterization and the recognition of graph classes. A popular
way to characterize a graph class is to list a minimal set of forbidden induced subgraphs …

Several heuristics and an exact branch-and-bound algorithm are described for the fixed
linear crossing number problem (FLCNP). An experimental study comparing the heuristics …

We survey known results and propose open problems on the biplanar crossing number. We
study biplanar crossing numbers of specific families of graphs, in particular, of complete …