Degree conditions for spanning structures in dense graphs

Abstract: A classic theorem of Dirac (1952) states that a graph in which every vertex is connected to at least half of the other vertices contains a Hamilton cycle. Over the years, this result has been generalised in several ways. Some generalisations weaken the assumptions (by not requiring every vertex to have large minimum degree), and other generalisations strengthen the outcome (by considering spanning structures which are not cycles). We investigate the combination of these two directions, and find cycles and other spanning structures under various degree conditions. Along the way, we recover known results and obtain many new ones. Joint work with Richard Lang.

combinatoricsprobability

Audience: researchers in the topic

Extremal and probabilistic combinatorics webinar

Series comments: We've added a password: concatenate the 6 first prime numbers (hence obtaining an 8-digit password).