Related papers: Testing isomorphism of chordal graphs of bounded l…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
For a fixed number of colors, we show that, in node-weighted split graphs, cographs, and graphs of bounded tree-width, one can determine in polynomial time whether a proper list-coloring of the vertices of a graph such that the total weight…
An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs. Recall that the…
A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is…
In this paper, we propose algorithms for the graph isomorphism (GI) problem that are based on the eigendecompositions of the adjacency matrices. The eigenvalues of isomorphic graphs are identical. However, two graphs $ G_A $ and $ G_B $ can…
A $b$-coloring of a graph is a proper vertex coloring such that each color class contains a vertex that sees all other colors in its neighborhood. The $b$-coloring problem, in which the task is to decide whether a graph admits a…
The \emph{linear vertex arboricity} of a graph is the smallest number of sets into which the vertices of a graph can be partitioned so that each of these sets induces a linear forest. Chaplick et al. [JoCG 2020] showed that, somewhat…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
Pedigree graphs, or family trees, are typically constructed by an expensive process of examining genealogical records to determine which pairs of individuals are parent and child. New methods to automate this process take as input genetic…
In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a…
We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that these series can be evaluated on graphs and count occurrences…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor. We introduce a…
Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence…
Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to biological and biomedical problems. The graph matching…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely…
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph $G$ to edge-coloured graph $H$ is a vertex-mapping from $G$ to…