Related papers: Practical and Efficient Split Decomposition via Gr…

Given a graph $G=(V,E)$ with arboricity $\alpha$, we study the problem of decomposing the edges of $G$ into $(1+\epsilon)\alpha$ disjoint forests in the distributed LOCAL model. Barenboim and Elkin [PODC `08] gave a LOCAL algorithm that…

A graph G is an NG-graph if \chi(G) + \chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split…

This is a new and short proof of the main theorem of classical structure tree theory. Namely, we show the existence of certain automorphism-invariant tree-decompositions of graphs based on the principle of removing finitely many edges. This…

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…

We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…

We propose a new and strengthened Branch-and-Bound (BnB) algorithm for the maximum common (connected) induced subgraph problem based on two new operators, Long-Short Memory (LSM) and Leaf vertex Union Match (LUM). Given two graphs for which…

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like…

Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lov\'asz and Plummer developed a decomposition theory for graphs with perfect…

Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first…

Graph-cuts are widely used in computer vision. In order to speed up the optimization process and improve the scalability for large graphs, Strandmark and Kahl introduced a splitting method to split a graph into multiple subgraphs for…

Knowledge Graph Completion (KGC), which aims to infer missing or incomplete facts, is a crucial task for KGs. However, integrating the vital structural information of KGs into Large Language Models (LLMs) and outputting predictions…

Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In previous works, a linear-time algorithm was introduced to partition dual graphs into maximally connected components called…

The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…

In this paper, we study split graphs and related classes of graphs from the perspective of their sequence of vertex degrees and an associated lattice under majorization. Following the work of Merris in 2003, we define blocks…

Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…

Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core…