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Color refinement is an important technique that works very well in practice for the graph isomorphism problem. Tinhofer graphs are the class of graphs for which refinement together with individualization correctly tests graph isomorphism…
We investigate the power of counting in Group Isomorphism. We first leverage the count-free variant of the Weisfeiler--Leman Version I algorithm for groups (Brachter & Schweitzer, LICS 2020) in tandem with limited non-determinism and…
We study the minimum size $f$ of a feedback vertex set in directed and undirected $n$-vertex graphs of given degeneracy or treewidth. In the undirected setting the bound $\frac{k-1}{k+1}n$ is known to be tight for graphs with bounded…
Monadic second order logic (MSO2) plays an important role in parameterized complexity due to the Courcelle's theorem. This theorem states that the problem of checking if a given graph has a property specified by a given MSO2 formula can be…
Cliquewidth is a dense analogue of treewidth. It can be deduced from recent results by Hickingbotham [arXiv:2501.10840] and Nguyen, Scott, and Seymour [arXiv:2501.09839] that graphs of bounded cliquewidth are quasi-isometric to graphs of…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
A stability result due to Ren, Wang, Wang and Yang [SIAM J. Discrete Math. 38 (2024)] shows that if $3\le r \le 2k$ and $n\ge 318 (r-2)^2k$, and $G$ is a $C_{2k+1}$-free graph on $n$ vertices with $e(G)\ge \lfloor {(n-r+1)^2}/{4}\rfloor +{r…
A vertex set $S$ is a generalized $k$-independent set if the induced subgraph $G[S]$ contains no tree on $k$ vertices. The generalized $k$-independence number $\alpha_k(G)$ is the maximum size of such a set. For a tree $T$ with $n$…
We prove new parameterized complexity results for the FO Model Checking problem on a well-known generalization of interval and circular-arc graphs: the class of $H$-graphs, for any fixed multigraph $H$. In particular, we research how the…
For an infinite class of finite graphs of unbounded size, we define a limit object, to be called a $\textit{wide limit}$, relative to some computationally restricted class of functions. The limit object is a first order Boolean-valued…
We study the formula complexity of Iterated Sub-Permutation Matrix Multiplication, the logspace-complete problem of computing the product of $k$ $n$-by-$n$ Boolean matrices with at most a single $1$ in each row and column. For all $d \le…
Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…
Graph editing problems offer an interesting perspective on sub- and supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of…
In the \emph{$k$-Diameter-Optimally Augmenting Tree Problem} we are given a tree $T$ of $n$ vertices as input. The tree is embedded in an unknown \emph{metric} space and we have unlimited access to an oracle that, given two distinct…
The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…
We first introduce the class of bipartite absolute retracts with respect to tree obstructions with at most $k$ leaves. Then, using the theory of homomorphism duality, we show that this class of absolute retracts coincides exactly with the…
Graph super-resolution, the task of inferring high-resolution (HR) graphs from low-resolution (LR) counterparts, is an underexplored yet crucial research direction that circumvents the need for costly data acquisition. This makes it…
We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k+4. This is the first algorithm…
Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…