Related papers: Maximal Pivots on Graphs with an Application to Ge…
We describe a graph reduction operation, generalizing three graph reduction operations related to gene assembly in ciliates. The graph formalization of gene assembly considers three reduction rules, called the positive rule, double rule,…
Gene assembly in ciliates is one of the most involved DNA processings going on in any organism. This process transforms one nucleus (the micronucleus) into another functionally different nucleus (the macronucleus). We continue the…
We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the…
We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
We study the interplay between principal pivot transform (pivot) and loop complementation for graphs. This is done by generalizing loop complementation (in addition to pivot) to set systems. We show that the operations together, when…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…
Gene assembly is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been…
Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the…
A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more…
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to…
In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a…
In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…
Generative models of graph structure have applications in biology and social sciences. The state of the art is GraphRNN, which decomposes the graph generation process into a series of sequential steps. While effective for modest sizes, it…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
We consider the problem of determining the inducibility (maximum possible asymptotic density of induced copies) of oriented graphs on four vertices. We provide exact values for more than half of the graphs, and very close lower and upper…
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that…