相关论文: Two faces of greedy leaf removal procedure on grap…

The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…

Since many NP-complete graph problems have been shown polynomial-time solvable when restricted to claw-free graphs, we study the problem of determining the distance of a given graph to a claw-free graph, considering vertex elimination as…

A typical way in which network data is recorded is to measure all the interactions among a specified set of core nodes; this produces a graph containing this core together with a potentially larger set of fringe nodes that have links to the…

Graph Neural Networks (GNNs) have proven to excel in predictive modeling tasks where the underlying data is a graph. However, as GNNs are extensively used in human-centered applications, the issue of fairness has arisen. While edge deletion…

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…

We consider the problem of finding a large rainbow matching in a random graph with randomly colored edges. In particular we analyze the performance of two greedy algorithms for this problem. The algorithms we study are colored versions of…

A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are of distance 2 from each other. The Square Root problem is that of deciding whether a given graph admits a…

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,…

The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed…

We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted after applying this procedure a fixed number of times by using…

We consider the problem of online graph colouring. Whenever a node is requested, a colour must be assigned to the node, and this colour must be different from the colours of any of its neighbours. According to the greedy algorithm the node…

We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

This paper describes a graph clustering algorithm that aims to minimize the normalized cut criterion and has a model order selection procedure. The performance of the proposed algorithm is comparable to spectral approaches in terms of…

Line graphs are an alternative representation of graphs where each vertex of the original (root) graph becomes an edge. However not all graphs have a corresponding root graph, hence the transformation from graphs to line graphs is not…

Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…

We describe a new random greedy algorithm for generating regular graphs of high girth: Let $k\geq 3$ and $c \in (0,1)$ be fixed. Let $n \in \mathbb{N}$ be even and set $g = c \log_{k-1} (n)$. Begin with a Hamilton cycle $G$ on $n$ vertices.…

The Grundy number of a graph is the maximum number of colours used by the "First-Fit" greedy colouring algorithm over all vertex orderings. Given a vertex ordering $\sigma= v_1,\dots,v_n$, the "First-Fit" greedy colouring algorithm colours…

The irrelevant vertex technique provides a powerful tool for the design of parameterized algorithms for a wide variety of problems on graphs. A common characteristic of these problems, permitting the application of this technique on…

Structural parameters of graph (such as degeneracy and arboricity) had rarely been considered when designing algorithms for $\textit{(edge) clique cover}$ problems. Taking degeneracy of graph into account, we present a greedy framework and…