Related papers: Graph Isomorphism for $(H_1,H_2)$-free Graphs: An …
It was recently shown \cite{STV} that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we…
We consider two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities p_1,p_2. In particular, (i) we prove a sharp threshold result for the appearance of G_{n,p_1}…
We introduce the class of interval $H$-graphs, which is the generalization of interval graphs, particularly interval bigraphs. For a fixed graph $H$ with vertices $a_1,a_2,\dots,a_k$, we say that an input graph $G$ with given partition…
Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially…
We prove that for every integer $t\geq 1$ there exists an integer $c_t\geq 1$ such that every $n$-vertex even-hole-free graph with no clique of size $t$ has treewidth at most $c_t\log{n}$. This resolves a conjecture of Sintiari and…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
We study the problem of computing the parity of the number of homomorphisms from an input graph $G$ to a fixed graph $H$. Faben and Jerrum [ToC'15] introduced an explicit criterion on the graph $H$ and conjectured that, if satisfied, the…
The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant G(n,W) of the Erdos-Renyi random graph. Here we study the clique number of these random graphs. We establish the concentration of…
A graph K is square-free if it contains no four-cycle as a subgraph. A graph K is multiplicative if GxH -> K implies G -> K or H -> K, for all graphs G,H. Here GxH is the tensor (or categorical) graph product and G -> K denotes the…
In line with the recent development in topological graph theory, we are considering undirected graphs that are allowed to contain {\em multiple edges}, {\em loops}, and {\em semi-edges}. A graph is called {\em simple} if it contains no…
We study the isomorphism problem for random hypergraphs. We show that it is solvable in polynomial time for the binomial random $k$-uniform hypergraph $H_{n,p;k}$, for a wide range of $p$. We also show that it is solvable w.h.p. for random…
We study the complexity of graph problems on graphs defined on groups, especially power graphs. We observe that an isomorphism invariant problem, such as Hamiltonian Path, Partition into Cliques, Feedback Vertex Set, Subgraph Isomorphism,…
A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of…
A result due to Gy\'arf\'as, Hubenko, and Solymosi (answering a question of Erd\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\binom{n}{2}$ edges, then $G$ has a…
We prove that isomorphism of tournaments of twin width at most $k$ can be decided in time $k^{O(\log k)}n^{O(1)}$. This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in…
We establish an isomorphism between the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ in depth two modulo higher depth and the cohomology of the two-loop part of the graph complex of internally connected graphs…
Subgraph counting is a fundamental and well-studied problem whose computational complexity is well understood. Quite surprisingly, the hypergraph version of subgraph counting has been almost ignored. In this work, we address this gap by…
A recent paper by the authors (ITCS'26) initiates the study of the Triangle Detection problem in graphs avoiding a fixed pattern $H$ as a subgraph and proposes a \emph{dichotomy hypothesis} characterizing which patterns $H$ make the…
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…