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 some …

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 …

Given a set \calF of graphs, a graph G is \calF‐free if G does not contain any member of \calF
as an induced subgraph. We say that \calF is a degree‐sequence‐forcing set if, for each …

The fractional analogues of domination and packing in a graph form an interesting pair of
dual linear programs, in that the feasible vectors for both LPs have interpretations as …

A graph G is pancyclic if it contains cycles of each length ℓ, 3≤ ℓ≤| V (G)|. The generalized
bull B (i, j) is obtained by associating one endpoint of each of the paths Pi+ 1 and Pj+ 1 with …

Let H be a family of connected graphs. A graph G is said to be H-free if G is H-free for every
graph H in H. In Aldred et al.(2010)[1], it was pointed that there is a family of connected …

A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to. We show that if
G is 4‐connected, claw‐free, and P10‐free, then G is either pancyclic or it is the line graph of …

Hamiltonian graph theory has been widely studied as one of the most important problems in
graph theory. In this thesis, we work on generalizations of hamiltonian graph theory, and …

Abstract In 1984, Matthews and Sumner conjectured that every 4-connected, claw-free
graph contains a Hamiltonian cycle. This still unresolved conjecture has been the motivation …

Given a set FF of graphs, a graph GG is F F-free if GG does not contain any member of FF as
an induced subgraph. We say that FF is a degree-sequence-forcing set if, for each graph GG …