Related papers: Graph isomorphism in quasipolynomial time paramete…
The kTree problem is a special case of Subgraph Isomorphism where the pattern graph is a tree, that is, the input is an $n$-node graph $G$ and a $k$-node tree $T$, and the goal is to determine whether $G$ has a subgraph isomorphic to $T$.…
We prove that there is a graph isomorphism test running in time $n^{\operatorname{polylog}(h)}$ on $n$-vertex graphs excluding some $h$-vertex graph as a minor. Previously known bounds were $n^{\operatorname{poly}(h)}$ (Ponomarenko, 1988)…
We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
The group isomorphism problem in computational complexity asks whether two finite groups given by their Cayley tables are isomorphic or not. Although polynomial-time isomorphism tests exist for many specific types of groups, no general…
We claimed that there is a polynomial algorithm to test if two graphs are isomorphic. But the algorithm is wrong. It only tests if the adjacency matrices of two graphs have the same eigenvalues. There is a counterexample of two…
Graphs with high symmetry or regularity are the main source for experimentally hard instances of the notoriously difficult graph isomorphism problem. In this paper, we study the computational complexity of isomorphism testing for line…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [Bod90],[YBFT99]. We give restricted space algorithms for these problems proving the…
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
The isomorphism problem for graphs (GI) and the isomorphism problem for groups (GrISO) have been studied extensively by researchers. The current best algorithms for both these problems run in quasipolynomial time. In this paper, we study…
We give a fixed-parameter tractable algorithm that, given a parameter $k$ and two graphs $G_1,G_2$, either concludes that one of these graphs has treewidth at least $k$, or determines whether $G_1$ and $G_2$ are isomorphic. The running time…
We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)}…
The graph isomorphism problem is considered. We assign modified $n$-variable characteristic polynomials for graphs and reduce the graph isomorphism problem to the problem of the polynomials isomorphism. It is required to find out, is there…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
The boxicity of a graph $G$ is the minimum dimension $d$ that admits a representation of $G$ as the intersection graph of a family of axis-parallel boxes in $\mathbb{R}^d$. Computing boxicity is an NP-hard problem, and there are few known…