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We study Subgraph Isomorphism on graph classes defined by a fixed forbidden graph. Although there are several ways for forbidding a graph, we observe that it is reasonable to focus on the minor relation since other well-known relations lead…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
The min-rank of a graph was introduced by Haemers (1978) to bound the Shannon capacity of a graph. This parameter of a graph has recently gained much more attention from the research community after the work of Bar-Yossef et al. (2006). In…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
A Cayley graph over a group G is said to be central if its connection set is a normal subset of G. It is proved that for any two central Cayley graphs over explicitly given almost simple groups of order n, the set of all isomorphisms from…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues…
We make advances towards a structural characterisation of the signed graphs $H$ for which the list switch $H$-colouring problem $\operatorname{LSwHom}(H)$ problem is polynomial time solvable. We conjecture a characterisation for signed…
Two graphs $G$ and $H$ are homomorphism indistinguishable over a graph class $\mathcal{F}$ if they admit the same number of homomorphisms from every graph $F \in \mathcal{F}$. Many graph isomorphism relaxations such as (quantum) isomorphism…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Subgraph isomorphism is a well-known NP-hard problem which is widely used in many applications, such as social network analysis and knowledge graph query. Its performance is often limited by the inherent hardness. Several insightful works…
This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two…
We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
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…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
A pair of graphs $(\Gamma,\Sigma)$ is said to be stable if the full automorphism group of $\Gamma\times\Sigma$ is isomorphic to the product of the full automorphism groups of $\Gamma$ and $\Sigma$ and unstable otherwise, where…
An $H$-graph is an intersection graph of connected subgraphs of a suitable subdivision of a fixed graph $H$. Many important classes of graphs, including interval graphs, circular-arc graphs, and chordal graphs, can be expressed as…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…