This article is intended as a survey, updating earlier surveys in the area. For completeness
of the presentation of both particular questions and the general area, it also contains …

In this survey we have attempted to bring together most of the results and papers that deal
with toughness related to cycle structure. We begin with a brief introduction and a section on …

Generalizations of Dirac’s theorem in Hamiltonian graph theory—A survey - ScienceDirect
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A chord of a cycle C is an edge between two non-consecutive vertices of the cycle. A cycle C
in a graph G is chorded if the vertex set of C induces at least one chord. In 1961 Posa …

There has been extensive research on cycle lengths in graphs with large minimum degree.
In this paper, we obtain several results that are tight in this area. Let G be a graph with …

A graph G on n vertices is pancyclic if it contains cycles of length t for all 3≦t≦n. In this
paper we prove that for any fixed ϵ>0, the random graph G(n,p) with p(n)≫n^-1/2 (ie, with …

A sufficient condition for all short cycles Page 1 ELSEVIER DISCRETE APPLIED Discrete
Applied Mathematics 79 (1997) 63-66 MATHEMATICS A sufficient condition for all Stephan …

In this paper, we study the upper size Ramsey number u (G 1, G 2), defined by Erdős and
Faudree, as well as the star-critical Ramsey number r∗(G 1, G 2), defined by Hook and …

Abstract Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is
very fast developing, and in this long but relatively short survey we select some of those …

Let B_n^(k) be the book graph which consists of n copies of K_k+1 all sharing a common
K_k, and let C_m be a cycle of length m. In this paper, we first determine the exact value of …