Related papers: Split decomposition and graph-labelled trees: char…

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…

Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested…

Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…

We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement…

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…

We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the…

A graph is perfectly divisible if for each of its induced subgraph $H$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\omega(H[B]) < \omega(H)$, and a graph $G$ is perfectly weight divisible if for every…

A hypergraph is said to be $1$-Sperner if for every two hyperedges the smallest of their two set differences is of size one. We present several applications of $1$-Sperner hypergraphs and their structure to graphs. In particular, we…

This paper proposes a novel algorithm for the problem of structural image segmentation through an interactive model-based approach. Interaction is expressed in the model creation, which is done according to user traces drawn over a given…

We introduce a characterization for split graphs by using edge contraction. Then, we use it to prove that any ($2K_{2}$, claw)-free graph with $\alpha(G) \geq 3$ is a split graph. Also, we apply it to characterize any pseudo-split graph.…

The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$…

A graph is said to be well-covered if all its maximal independent sets are of the same size. In 1999, Yamashita and Kameda introduced a subclass of well-covered graphs, called localizable graphs and defined as graphs having a partition of…

We develop a new algorithmic framework for designing approximation algorithms for cut-based optimization problems on capacitated undirected graphs that undergo edge insertions and deletions. Specifically, our framework dynamically maintains…

The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call the junction-tree expander and junction-tree collapser…

The notions of bounded-size and quasibounded-size decompositions with bounded treedepth base classes are central to the structural theory of graph sparsity introduced by two of the authors years ago, and provide a characterization of both…

In this paper we look at the problem of adjacency labeling of graphs. Given a family of undirected graphs the problem is to determine an encoding-decoding scheme for each member of the family such that we can decode the adjacency…

A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The decision problem whether a graph has a disconnected cut is called Disconnected Cut. This problem is closely related to several…