Choongbum Lee

Dirac's theorem for random graphs

A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{align*}\left\lceil n/2 \right\rceil\end{align*} \end{document} **image** is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if p ≫ log n/n, then a.a.s. every subgraph of G(n,p) with minimum degree at least (1/2 + o (1))np is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge probability p and the value of the constant 1/2 are asymptotically best possible.

Resilient Pancyclicity of Random and Pseudorandom Graphs

A graph

Bandwidth theorem for random graphs

G

Rank-width of random graphs

on

Ordered Ramsey numbers

n

Robust Hamiltonicity of Dirac graphs

vertices is pancyclic if it contains cycles of length

Long paths and cycles in random subgraphs of graphs with large minimum degree

t

ShapeFit and ShapeKick for Robust, Scalable Structure from Motion

for all

Self-Similarity of Graphs

3\leq t\leq n

Packing spanning graphs from separable families

. In this paper we prove that for any fixed