Related papers: Isomorphism for Random $k$-Uniform Hypergraphs

We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…

Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.

For any given integer $r\geqslant 3$, let $k=k(n)$ be an integer with $r\leqslant k\leqslant n$. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. Let…

In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the…

The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…

In this paper, we study the homology of the coloring complex and the cyclic coloring complex of a complete $k$-uniform hypergraph. We show that the coloring complex of a complete $k$-uniform hypergraph is shellable, and we determine the…

Clique-width is a well-studied graph parameter. For graphs of bounded clique-width, many problems that are NP-hard in general can be polynomial-time solvable. The fact motivates several studies to investigate whether the clique-width of…

Motivated by the wide-ranging applications of Hamiltonian decompositions in distributed computing, coded caching, routing, resource allocation, load balancing, and fault tolerance, our work presents a comprehensive design for Hamiltonian…

Extending the notion of (random) $k$-out graphs, we consider when the $k$-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each $r$ there is a $k=k(r)$ such that the $k$-out $r$-uniform…

We consider the complexity of finding weighted homomorphisms from intersection graphs of curves (string graphs) with $n$ vertices to a fixed graph $H$. We provide a complete dichotomy for the problem: if $H$ has no two vertices sharing two…

In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$…

Let $K_n$ be the complete graph with $n$ vertices and $c_1, c_2, ..., c_r$ be $r$ different colors. Suppose we randomly and uniformly color the edges of $K_n$ in $c_1, c_2, ..., c_r$. Then we get a random graph, denoted by…

Correspondence homomorphisms are both a generalization of standard homomorphisms and a generalization of correspondence colourings. For a fixed target graph $H$, the problem is to decide whether an input graph $G$, with each edge labeled by…

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…

A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.

The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can…

In this paper, we give a reduced formula of the characteristic polynomial of $k$-uniform hypergraphs with a pendant edge. And the explicit characteristic polynomial and all distinct eigenvalues of $k$-uniform hyperpath are given.

Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$ can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$…

We provide a combinatorial characterization of all testable properties of $k$-uniform hypergraphs ($k$-graphs for short). Here, a $k$-graph property $P$ is testable if there is a randomized algorithm which makes a bounded number of edge…

Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be…