Related papers: Longest paths in random hypergraphs

The size-Ramsey number $R^{(k)}(H)$ of a $k$-uniform hypergraph $H$ is the minimum number of edges in a $k$-uniform hypergraph $G$ with the property that every `$2$-edge coloring' of $G$ contains a monochromatic copy of $H$. For $k\ge2$ and…

The $k$-Detour problem is a basic path-finding problem: given a graph $G$ on $n$ vertices, with specified nodes $s$ and $t$, and a positive integer $k$, the goal is to determine if $G$ has an $st$-path of length exactly $\text{dist}(s, t) +…

Given a graph $G$, we denote by $f(G,u_0,k)$ the number of paths of length $k$ in $G$ starting from $u_0$. In graphs of maximum degree 3, with edge weights $i.i.d.$ with $exp(1)$, we provide a simple proof showing that (under the assumption…

Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…

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…

For integers $k \geq 3$ and $r\geq 2$, we show that for every $\alpha> 0$, there exists $\varepsilon > 0$ such that the union of $k$-uniform hypergraph on $n$ vertices with minimum codegree at least $\alpha n$ and a binomial random…

Finding a Maximum Clique is a classic property test from graph theory; find any one of the largest complete subgraphs in an Erd\"os-R\'enyi G(N, p) random graph. We use Maximum Clique to explore the structure of the problem as a function of…

In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…

We give almost tight conditional lower bounds on the running time of the kHyperPath problem. Given an $r$-uniform hypergraph for some integer $r$, kHyperPath seeks a tight path of length $k$. That is, a sequence of $k$ nodes such that every…

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…

The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…

We study a variant of the Erd\H{o}s Matching Problem in random hypergraphs. Let $\mathcal{K}_p(n,k)$ denote the Erd\H{o}s-R\'enyi random $k$-uniform hypergraph on $n$ vertices where each possible edge is included with probability $p$. We…

Graphs have been commonly used to model many applications. A natural problem which abstracts applications such as itinerary planning, playlist recommendation, and flow analysis in information networks is that of finding the heaviest path(s)…

Multiple-choice load balancing has been a topic of intense study since the seminal paper of Azar, Broder, Karlin, and Upfal. Questions in this area can be phrased in terms of orientations of a graph, or more generally a k-uniform random…

We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we…

Finding dense subgraphs is a core problem in graph mining with many applications in diverse domains. At the same time many real-world networks vary over time, that is, the dataset can be represented as a sequence of graph snapshots. Hence,…

We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as \emph{online sprinkling}. As an illustrative application of this method, we show that for any fixed integer $k\geq 3$, the binomial…

If the edges of the complete graph $K_n$ are totally ordered, a simple path whose edges are in ascending order is called increasing. The worst-case length of the longest increasing path has remained an open problem for several decades, with…

We present a modification of the Depth first search algorithm, suited for finding long induced paths. We use it to give simple proofs of the following results. We show that the induced size-Ramsey number of paths satisfies…

We investigate the emergence of spanning structures in sparse pseudo-random $k$-uniform hypergraphs, using the following comparatively weak notion of pseudo-randomness. A $k$-uniform hypergraph $H$ on $n$ vertices is called…