Sentence examples for a cycle of length from inspiring English sources

If C is a cycle of length at most 4, then we are done.

Let D denote the graph consisting of a cycle of length 4 with a pendant edge.

Note that a cycle of length l, starting from v, consists of a sequence of l+1 nodes, two of which are v and others are distinct.

Now, suppose that the former occurs, i.e., P w +P z +〈w,v j,z〉 contains a cycle of length at most ℓ w +ℓ z +2.

In this study, a cycle of length l is defined as a path visiting a node twice and visiting other l−2 nodes exactly once.

We get a contradiction as this implies G has a cycle of length 4. Therefore we may assume v i ∉{w,z}.

This section introduces the edge-covering problem and then presents an algorithm that solves it for two processes on any connected graph G that has a cycle of odd length.

In this paper, we prove that if D is a pairwise balanced design, PBD v,K,λ), with arbitrary index λ⩾1 and maxK⩽λminK, then GD contains a cycle of each length ℓ= 3,4,…,|V(GD |.

In this paper, we prove that if D is a balanced incomplete block design, BIBD v,k,λ), with arbitrary index λ, then GD contains a cycle of each length ℓ=3,4,…,|V(GD |.

A cycle in C 4 4 ( v ) consists of a simple cycle of length 3, in which the first and last nodes are v.

Let C be a chordless cycle of length at least four in GΔ.