To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding
problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic …

The protection routing uses the multi-paths technique for integrating route discovery and
route maintenance mechanisms in a network, and thus it can tolerate the failure of one …

One of the important issues in evaluating an interconnection network is to study the fault-
tolerant Hamiltonian cycle and Hamiltonian path embedding problems. The-ary-cube …

Given a graph G, let S and T be two disjoint vertex subsets of equal size k in G. A many-to-
many k-disjoint path cover of G joining S and T is a set of k vertex-disjoint paths between S …

Independent spanning trees (ISTs) on networks have applications in networks such as
reliable communication protocols, the multi-node broadcasting, one-to-all broadcasting …

Multiple independent spanning trees (ISTs) can be used for data broadcasting in networks,
which can provide advantageous performances, such as the enhancement of fault …

Given two disjoint vertex-sets, S={s 1,…, sk} and T={t 1,…, tk} in a graph, a paired many-to-
many k-disjoint path cover joining S and T is a set of pairwise vertex-disjoint paths {P 1,…, P …

The n-dimensional hypercube network Qn is one of the most popular interconnection
networks since it has simple structure and is easy to implement. The n-dimensional locally …

Cycle-embedding is an important issue in evaluating the efficiency of interconnection
networks and is also an extension of the theoretical research on Hamiltonicity. In this paper …

A graph G is said to be conditional k-edge-fault pancyclic if after removing k faulty edges
from G, under the assumption that each node is incident to at least two fault-free edges, the …