When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

Primarily intended for research mathematicians and computer scientists, Combinatorics and
Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students …

Acyclic digraphs are widely used for representing hierarchical structures. Examples include
PERT networks, subroutine-call graphs, family trees, organization charts, Hasse diagrams …

A standard problem in combinatorial theory is to characterize structures which satisfy a
certain property by providing a minimum list of forbidden substructures, for example …

A polynomial-time algorithm for testing if a triconnected directed graph has an upward
drkwing is presented. An upward drkwing is a planar drkwing such that all the edges flow in …

A digraph is upward planar if it has a planar drawing such that all the edges are monotone
with respect to the vertical direction. Testing upward planarity and constructing upward …

Ordered sets are ubiquitous in mathematics and have significant applications in computer
science, statistics, biology and the social sciences. As the first book to deal exclusively with …

We obtain new parameterized algorithms for the classical problem of determining whether a
directed acyclic graph admits an upward planar drawing. Our results include a new fixed …

This paper surveys results concerning packing/covering parameters and representation
parameters of graphs and posets. We start from the poset parameters known as width and …

In 1930, E. Szpilrajn proved that any order relation on a set X can be extended to a linear
order on X. It also follows that any order relation is the intersection of its linear extensions. B …