Related papers: Supersolvable saturated matroids and chordal graph…
Rough sets are efficient for data pre-processing in data mining. Matroids are based on linear algebra and graph theory, and have a variety of applications in many fields. Both rough sets and matroids are closely related to lattices. For a…
A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a…
We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…
We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the…
This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…
A graph is called equimatchable if all of its maximal matchings have the same size. Frendrup et al. [8] provided a characterization of equimatchable graphs with girth at least $5$. In this paper, we extend this result by providing a…
Let G be a chordal graph, X(G) the complement of the associated complex arrangement and Gamma(G) the fundamental group of X(G). We show that Gamma(G) is a limit of colored braid groups over the poset of simplices of G. When G = G_T is the…
We give a structure theorem for Cohen Macaulay monomial ideals of codimension 2, and describe all possible relation matrices of such ideals. In case that the ideal has a linear resolution, the relation matrices can be identified with the…
In this paper we prove the conjectured upper bound for Castelnuovo-Mumford regularity of binomial edge ideals posed in [23], in the case of chordal graphs. Indeed, we show that the regularity of any chordal graph G is bounded above by the…
We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of $M$ is already determined by the…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
A simple topological graph $G$ is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. $G$ is called saturated if no further edge can be added without…
A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set if it is a maximum stable set of the subgraph of G spanned by the union of S and N(S), where N(S) is the neighborhood of S. A matching M is…
An instance of the super-stable matching problem with incomplete lists and ties is an undirected bipartite graph $G = (A \cup B, E)$, with an adjacency list being a linearly ordered list of ties. Ties are subsets of vertices equally good…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is bipartite if and only if its Petrie dual is orientable. In this paper, we first introduce the…
We consider the following problem closely related to graph isomorphism. In a simplified version, the task is to compute the automorphism group of a given set family (or a hypergraph), that is, the group of all automorphisms of the given…
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete…
Many properties of simple finite dimensional gl(m|n)-modules may be better understood by assigning weight diagrams to the highest weights with respect to a given base of simple roots. In this paper we consider bases that are compatible with…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…