… cycles of specified length in finite undirected graphs and with the question of how this depends
on the numbers of vertit.¢s and edges ~ ulje graph, … Erdiss that every graph of order n and …

… How many simple cycles and how many Hamiltonian cycles can there be in a planar … cycles
and of Hamiltonian cycles in a graph G we define Cs(n) = max{Cs(G) | G is a planar graph on …

… on the distribution of the lengths of cycles in graphs, as well as related problems on chromatic
number and girth, counting graphs … by many conjectures of Erdős [38] stating that a graph …

… For a graph G, we define the cycle spectrum CSGfi of G as the sequence ‘1 < ¡¡¡ < ‘r of
lengths of cycles in G. The study of cycles in graphs has long been fundamental, and many …

… graph of minimum degree at least three contains a cycle … on the average degree of an n-vertex
graph with no cycle of even length in a prescribed infinite sequence of integers. For many …

… Examples of graphs with large girth which … graph theory, in studies of graphs with high
degree of symmetry, and in designs of communication networks. There are many references on …

… many cubic graphs with exactly one longest cycle of length p – k. On the other hand, if the
longest cycle … We consider the questions: How many longest cycles must a cubic graph have, …

… with tighter bounds for graphs with few edges compared to ‘ (Lemma 6) and many edges (…
on a 4-cycle in G. Moreover, every 4-cycle C of a graph G is augmented and each edge on …

… on the expected length of the minimum-length fundamental-cycle set L(T~,,n), for certain "bad"
classes of graphs. It … As is the case with many of the polynomially bounded graph-theoretic …

… This property is so strong that many hamiltonian graphs are excluded. Consider the …
vertices on P, vi and v,+ i such that (v,, v,,,) EE(G) and (vi+i, v,,) EE(G), and so we obtain a cycle of …