Αποτελέσματα Αναζήτησης
1 Ιαν 2023 · The cycle spectrum of a given graph G is the lengths of cycles in G. In this paper, we introduce the following problem: determining the maximum number of edges of an n -vertex graph with given cycle spectrum.
You save hundreds of dollars and get FREE Service* for 90 Days with every bicycle purchased from a CycleSpectrum Bike Shop. (*covers labor, parts are additional cost) We’d like you to use our stores as a source of information. Nothing can replace the face-to-face relationship.
The cycle spectrum of a graph G is the set of lengths of cycles in G. A cycle containing all vertices of a graph is a spanning or Hamiltonian cycle, and a graph having such a cycle is a Hamiltonian graph. An n-vertex graph is pancyclic if its cycle spectrum is {3, . . . , n}. Our graphs have no loops or multiple edges.
The cycle spectrum of a graph G is the set of lengths of cycles in G. A cycle containing all vertices of a graph is a spanning or Hamiltonian cycle, and a graph having such a cycle is a
An n-vertex Hamiltonian graph G with 𝛿(𝐺)≥3 contains cycles of 𝑛 1−𝑜( ) different lengths. Our proof of Theorem 1.1 is constructive: It gives a polynomial-time algorithm for finding cycles of 𝑛 1−𝑜( ) different lengths in a Hamiltonian graph of minimum degree 3, provided a Hamilton cycle is specified. 2. A sketch and ...
This thesis contains several new results about cycle spectra of graphs. The cycle spectrum of a graph G is the set of lengths of cycles in G. We focus on conditions which imply a rich cycle spectrum. … Expand
How small can the cycle spectrum be? De nition Let f n(m)be the minimum size of the cycle spectrum of an n-vertex Hamiltonian graph with m edges. Theorem (Bondy (1971)) If G is an n-vertex Hamiltonian graph with m edges and m >n2=4, then G ispancyclic(has cycles of all lengths from 3 to n). Theorem (Entringer{Schmeichel (1988))
