14 research outputs found
Minimal Degree and (k,m)-Pancyclic Ordered Graphs
https://digitalcommons.memphis.edu/speccoll-faudreerj/1233/thumbnail.jp
A look at cycles containing specified elements of a graph
AbstractThis article is intended as a brief survey of problems and results dealing with cycles containing specified elements of a graph. It is hoped that this will help researchers in the area to identify problems and areas of concentration
On extremal hypergraphs for hamiltonian cycles
We study sufficient conditions for Hamiltonian cycles in hypergraphs, and
obtain both Tur\'an- and Dirac-type results. While the Tur\'an-type result
gives an exact threshold for the appearance of a Hamiltonian cycle in a
hypergraph depending only on the extremal number of a certain path, the
Dirac-type result yields a sufficient condition relying solely on the minimum
vertex degree.Comment: 13 page
Sets as graphs
The aim of this thesis is a mutual transfer of computational and structural results and techniques between sets and graphs. We study combinatorial enumeration of sets, canonical encodings, random generation, digraph immersions. We also investigate the underlying structure of sets in algorithmic terms, or in connection with hereditary graphs classes. Finally, we employ a set-based proof-checker to verify two classical results on claw-free graph
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete