### Resilient degree sequences with respect to Hamiltonicity in random graphs

Combinatorics Seminar

2nd April 2019, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

The local resilience of a graph with respect to a property P can be defined as the maximum number of edges incident to each vertex that an adversary can delete without destroying P. The resilience of random graphs with respect to various properties has received much attention in recent years, with a special emphasis on Hamiltonicity. Based on different sufficient degree conditions for Hamiltonicity, we investigate a notion of local resilience in which the adversary is allowed to delete a different number of edges at each vertex, and obtain some results which improve on previous results.

This is joint work with P. Condon, J. Kim, D. Kühn and D. Osthus.

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