Related papers: A Note on Edge Coalitions in Graphs
The edge clique cover number $ecc(G)$ of a graph $G$ is the size of the smallest set of complete subgraphs whose union covers all edges of $G$. It has been conjectured that all the simple graphs with independence number two satisfy…
Let $\mathcal{G}_{\alpha}$ be a hereditary graph class (i.e, every subgraph of $G_{\alpha}\in \mathcal{G}_{\alpha}$ belongs to $\mathcal{G}_{\alpha}$) such that every graph $G_{\alpha}$ in $\mathcal{G}_{\alpha}$ has minimum degree at most…
Let G=(V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v in V dominates its closed neighborhood N[v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v in V, there is…
The families EPT (resp. EPG) Edge Intersection Graphs of Paths in a tree (resp. in a grid) are well studied graph classes. Recently we introduced the graph classes Edge-Intersecting and Non-Splitting Paths in a Tree ENPT, and in a Grid…
The edge expansion of a graph is the minimum quotient of the number of edges in a cut and the size of the smaller one among the two node sets separated by the cut. Bounding the edge expansion from below is important for bounding the…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
Given an edge-coloring of a graph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. We define the palette index of a graph as the minimum number of distinct palettes, taken over all…
In the present paper a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is…
Graph neural networks have emerged as a powerful model for graph representation learning to undertake graph-level prediction tasks. Various graph pooling methods have been developed to coarsen an input graph into a succinct graph-level…
Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\in E(G)$ are said to have \emph{common edge} $e\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an endpoint…
Representation languages for coalitional games are a key research area in algorithmic game theory. There is an inherent tradeoff between how general a language is, allowing it to capture more elaborate games, and how hard it is…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…
In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…
We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in order to detect and prevent failures. Inspired by two…
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…