Related papers: An improved isomorphism test for bounded-tree-widt…
A T-graph (a special case of a chordal graph) is the intersection graph of connected subtrees of a suitable subdivision of a fixed tree T . We deal with the isomorphism problem for T-graphs which is GI-complete in general - when T is a part…
An $H$-graph is one representable as the intersection graph of connected subgraphs of a suitable subdivision of a fixed graph $H$, introduced by Bir\'{o}, Hujter and Tuza (1992). An $H$-graph is proper if the representing subgraphs of $H$…
This paper presents a linear FPT algorithm to find a tree decomposition with a 2-approximation of the treewidth with a significantly smaller exponential dependence on the treewidth. The algorithm runs in time $O(\text{poly}(k) 81^k n)$,…
Fixed parameter tractable (FPT) algorithms run in time f(p(x)) poly(|x|), where f is an arbitrary function of some parameter p of the input x and poly is some polynomial function. Treewidth, branchwidth, cliquewidth, NLC-width, rankwidth,…
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…
This paper presents a new graph isomorphism invariant, called $\mathfrak{w}$-labeling, that can be used to design a polynomial-time algorithm for solving the graph isomorphism problem for various graph classes. For example, all…
There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…
We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism (under group action) (SI) and Coset Intersection (CI) can be solved in quasipolynomial ($\exp((\log n)^{O(1)})$) time. The best previous bound…
We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…
The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
The Graph Isomorphism (GI) problem is a theoretically interesting problem because it has not been proven to be in P nor to be NP-complete. Babai made a breakthrough in 2015 when announcing a quasipolynomial time algorithm for GI problem.…
We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…
This article deals with new polynomial time algorithm for graph isomorphism testing.
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 clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…
We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a ``non-trivial'' approximation ratio (as a function of the number of vertices of the input…
In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…
Lubiw showed that several variants of Graph Isomorphism are NP-complete, where the solutions are required to satisfy certain additional constraints [SICOMP 10, 1981]. One of these, called Isomorphism With Restrictions, is to decide for two…