Related papers: Global certification via perfect hashing
Local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. For many classic global properties, like…
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes…
The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the graph, then the vertices are allowed to check their…
Detecting specific structures in a network has been a very active theme of research in distributed computing for at least a decade. In this paper, we start the study of subgraph detection from the perspective of local certification.…
We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove…
Given a network property or a data structure, a local certification is a labeling that allows to efficiently check that the property is satisfied, or that the structure is correct. The quality of a certification is measured by the size of…
Local certification consists in assigning labels (called \emph{certificates}) to the nodes of a network to certify a property of the network or the correctness of a data structure distributed on the network. The verification of this…
We introduce I/O-optimal certifying algorithms for bipartite graphs, as well as for the classes of split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a class member, the certifying algorithm returns a…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph $H$ we define the $H$-Hamiltonian number of a graph $G$. We will show that this concept is a generalization of…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
A 2-edge-colored graph or a signed graph is a simple graph with two types of edges. A homomorphism from a 2-edge-colored graph $G$ to a 2-edge-colored graph $H$ is a mapping $\varphi: V(G) \rightarrow V(H)$ that maps every edge in $G$ to an…
This note presents a new, elementary proof of a generalization of a theorem of Halin to graphs with unbounded degrees, which is then applied to show that every connected, countably infinite graph G with a subdegree-finite, infinite…
The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the…
In local certification, vertices of a $n$-vertex graph perform a local verification to check if a given property is satisfied by the graph. This verification is performed thanks to certificates, which are pieces of information that are…
A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL) are edge-weighted graphs G and the objective is to find…
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of…
Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…
We provide an upper bound to the number of graph homomorphisms from $G$ to $H$, where $H$ is a fixed graph with certain properties, and $G$ varies over all $N$-vertex, $d$-regular graphs. This result generalizes a recently resolved…