Related papers: An experimental approach: The graph of graphs
The {\em acyclic chromatic number} of a graph is the least number of colors needed to properly color its vertices so that none of its cycles has only two colors. The {\em acyclic chromatic index} is the analogous graph parameter for edge…
Maximal planar graph refers to the planar graph with the most edges, which means no more edges can be added so that the resulting graph is still planar. The Four-Color Conjecture says that every planar graph without loops is 4-colorable.…
We consider the problem of inferring a graphical Potts model on a population of variables, with a non-uniform number of Potts colors (symbols) across variables. This inverse Potts problem generally involves the inference of a large number…
E-graphs are a prominent data structure that has been increasing in popularity in recent years due to their expanding range of applications in various formal reasoning tasks. Often, they are used for equality saturation, a process of…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
In many practical applications the underlying graph must be as equitable colored as possible. A coloring is called equitable if the number of vertices colored with each color differs by at most one, and the least number of colors for which…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
A complete $k$-coloring of a graph $G=(V,E)$ is an assignment $\varphi:V\to\{1,\ldots,k\}$ of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one…
Many networked systems involve multiple modes of transport. Such systems are called multimodal, and examples include logistic networks, biomedical phenomena, manufacturing process and telecommunication networks. Existing techniques for…
The number of proper $q$-colorings of a graph $G$, denoted by $P_G(q)$, is an important graph parameter that plays fundamental role in graph theory, computational complexity theory and other related fields. We study an old problem of Linial…
Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion…
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for…
Matching mechanisms play a central role in operations management across diverse fields including education, healthcare, and online platforms. However, experimentally comparing a new matching algorithm against a status quo presents some…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte-Carlo simulations. We critically discuss…
Color representation is essential in computer vision and human-computer interaction. There are multiple color models available. The choice of a suitable color model is critical for various applications. This paper presents a review of color…