Cai and Yang initiated the systematic parameterized complexity study of the following set of problems around Eulerian graphs. For a given graph G and integer k, the task is to decide if G contains a (connected) subgraph with k vertices (edges) with all vertices of even (odd) degrees. They succeed to establish the parameterized complexity of all cases except two, when we ask about a connected k-...

Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a characterization of Seifert graphs in terms of Eulerian subgraphs. This charact...

The task of decoupling, i.e., removing unwanted internal couplings of a quantum system and its couplings to an environment, plays an important role in quantum control theory. There are many efficient decoupling schemes based on combinatorial concepts such as orthogonal arrays, difference schemes, and Hadamard matrices. So far these combinatorial decoupling schemes have relied on the ability to ...

A graph (digraph) G = (V,E) with a set T ⊆ V of terminals is called inner Eulerian if each nonterminal node v has even degree (resp. the numbers of edges entering and leaving v are equal). Cherkassky [1] and Lovász [15] showed that the maximum number of pairwise edge-disjoint T -paths in an inner Eulerian graph G is equal to 1 2 ∑ s∈T λ(s), where λ(s) is the minimum number of edges whose remova...

Graphs are among the most frequently used structures in Computer Science. Some of the properties that must be checked in many applications are connectivity, acyclicity and the Eulerian and Hamiltonian properties. In this work, we analyze how we can express these four properties with modal logics. This involves two issues: whether each of the modal languages under consideration has enough expres...

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.

This is a revision of the paper archived previously on August 22, 2002. It corrects a mistake in Sec. 8 concerning eccentricities of graphs. From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities are the vertice...

This paper describes a method for affine-invariant syntactic pattern recognition of geometric patterns using a new type of context-free graph grammar. The grammar accommodates variability in the geometric relations between parts of patterns; this variability is modelled using affine transformations and metric tensors. A parallel parsing algorithm is outlined, which is suitable for non-Eulerian ...

Multimatroids are combinatorial structures that generalize matroids and arise in the study of Eulerian graphs. We prove, by means of an efficient algorithm, a covering theorem for multimatroids. This theorem extends Edmonds’ covering theorem for matroids. It also generalizes a theorem of Jackson on the Euler tours of a 4-regular graph.