The family of random regular graphs is a classic topic in the realms of graph theory, combinatorics and computer science. In this paper we study the problem of learning random regular graphs from random paths. A random regular graph is generated uniformly at random and in a standard label-guided graph exploration setting, the edges incident from a node in the graph have distinct local labels. T...

Consider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that “hide” the cycle. Is it possible to unravel the structure, that is, to efficiently find a Hamiltonian cycle in G? We describe an O(n3 logn) steps algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly covers the “trouble spots” of G by a collection of ...

It is based on well-known network models Euler graph, Erdös and Renyi random graph, Watts-Strogatz small-world model and Barabási-Albert scale-free networks, and combined the unified hybrid network theoretical frame. One kind of network complexity pyramid with universality and diversity is constructed, described and reviewed. It is found that most unweighted and weighted models of network scien...

In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and seve...

We show that the threshold for the random graph Gn,p to contain the square of a Hamilton cycle is p = 1 √ n . This improves the previous results of Kühn and Osthus and also Nenadov and Škorić.

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis falls short of explaining this performance. Because this, “beyond worst-case analysis” algorithms has recently gained lot attention, including probabilistic algorithms. The instances many problems are essentially discrete metric space. Probabilistic such nevertheless mostly been cond...