Related papers: Dimension Reduction via Colour Refinement

List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek many in parallel. Our explorations have uncovered a…

Graph neural networks are designed to learn functions on graphs. Typically, the relevant target functions are invariant with respect to actions by permutations. Therefore the design of some graph neural network architectures has been…

In this work we present the notion of greyscale of a graph as a colouring of its vertices that uses colours from the real interval [0,1]. Any greyscale induces another colouring by assigning to each edge the non-negative difference between…

The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…

We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are…

It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…

Given a connected graph $G$ and its vertex $x$, let $U_x(G)$ denote the universal cover of $G$ obtained by unfolding $G$ into a tree starting from $x$. Let $T=T(n)$ be the minimum number such that, for graphs $G$ and $H$ with at most $n$…

Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…

The criteria for determining graph isomorphism are crucial for solving graph isomorphism problems. The necessary condition is that two isomorphic graphs possess invariants, but their function can only be used to filtrate and subdivide…

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…

We give a new, simple distributed algorithm for graph colouring in paths and cycles. Our algorithm is fast and self-contained, it does not need any globally consistent orientation, and it reduces the number of colours from $10^{100}$ to $3$…

The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…

In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, $\mathbb{Z}$-translates of itself. Refinable functions used in connection with wavelets are…

Given a graph $G$ and color set $\{1, \ldots, k\}$, a $\textit{proper coloring}$ is an assignment of a color to each vertex of $G$ such that no two vertices connected by an edge are given the same color. The problem of drawing a proper…

Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI,…

Automatic colorization of gray images with objects of different colors and sizes is challenging due to inter- and intra-object color variation and the small area of the main objects due to extensive backgrounds. The learning process often…

List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…

Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient graph coloring algorithm is of paramount importance. In this work we try to learn a good heuristic for coloring…