Sentence examples for exists a cycle from inspiring English sources

G is vertex-bipancyclic if for any vertex v∈V(G), there exists a cycle of every even length from 4 to |V(G)| that passes v.

If all the three cycles of (theta^{sigma}_{a,b,c}) are even, then there exists a cycle such that its sign is positive.

Since cycles of G are pairwise vertex-disjoint, there exists a cycle C in G such that all cycles of (G-C) lie in the same component, say (H _{1} ), of (G - C), and the other components of (G - C), say (H_{i}) ((i=2,ldots,p)), are trees.

Proof Suppose there exists a cycle containing only one palindrome.

However, the important thing is that there exists a cycle on which all three genes appear.

For example, for a SCC containing at least three genes, A i, A j, A k there exists a cycle A i →... → A j →... → A k →... → A i. The dots indicate that there are possibly other genes involved.

A rooted phylogenetic network N is called a galled network, if for every reticulation r in N and every pair of reticulation edges p and q with target node r there exists a tree cycle, that is, an undirected cycle in N that passes through p followed by q and otherwise contains only tree edges.

Now assume, by contradiction, that there exists a limit cycle.

If C0 < 0 and 0 < m - ( 1 - u + 2 d 2 d ⋅ 1 k d a u - d ) ≪ 1 hold, then system (2.1) exists a limit cycle around the small neighborhood of P2 x1, y1).

(1) If C0 > 0 and 0 < 1 - u + 2 d 2 d ⋅ 1 k d a u - d - m ≪ 1 hold, then system (2.1) exists a limit cycle around the small neighborhood of P2 x1, y1).

(2) If C0 < 0 and 0 < m - ( 1 - u + 2 d 2 d ⋅ 1 k d a u - d ) ≪ 1 hold, then system (2.1) exists a limit cycle around the small neighborhood of P2 x1, y1).