The Bristol One-Day Meeting in Combinatorics is an annual conference in Bristol with talks on a wide variety of topics within Combinatorics. Talks will cover recent developments in extremal and probabilistic combinatorics, additive combinatorics, structural graph theory and rigidity theory. The conference aims to be accessible to all and is free to attend.

Organisers:

Jesse Campion Loth (Bristol)
Sean Dewar (Bristol)
David Ellis (Bristol)
Tom Johnston (Bristol)

Speakers:

Carla Groenland (TU Delft).

Title: Infinite induced saturated graphs.

Abstract:

If H is a graph, we say that a graph G is H-free if it does not have H as induced subgraph. We show that for every finite graph H which is not a clique or a stable set, that there is a countable H-free graph G such that any graph G’ obtained from G by adding or removing edges in a “locally finite” manner does contain H as induced subgraph. This is based on joint work with Marthe Bonamy, Tom Johnston, Natasha Morrison and Alex Scott.

 

Sophie Huczynska (University of St Andrews).

Title: Additive triples in groups of odd prime order.

Abstract:

For a subset A of an additive group G,  a Schur triple in A is a triple of the form (a,b,a+b) in A^3.  Denote by r(A) the number of Schur triples of A. When r(A)=0, the set A is sum-free. Various questions about sum-free sets and extremal values of r(A) have received attention in the literature. The question of the minimum and maximum values of r(A) for a set A of fixed size in Z/(pZ) was resolved by Huczynska, Mullen and Yucas (2009) and independently by Samotij and Sudakov (2016). Lev (2001) and Chervak, Pikhurko and Staden (2019) addressed certain generalized versions of the Schur triple question for k-tuples in Z/(pZ). In this talk, I will explore this landscape and present recent work (with Jonathan Jedwab and Laura Johnson) on the generalization of the Schur triple problem to triples (a,b,a+b) \in A \times B \times B, where A and B are subsets of Z/(pZ).  Denote by r(A,B,B) the number of triples of this form; we obtain a precise description of its full spectrum of values and show constructively that each value in this spectrum can be realised when B is an interval of consecutive elements in Z/(pZ).

 

Tibor Jordan (Eötvös Loránd University).

Title: Highly connected orientations of graphs.

Abstract:

Thomassen conjectured in 1985 that for every positive integer k, there exists an integer f(k) such that every f(k)-connected graph has a k-connected orientation. In this talk, I will present the main ideas behind the recent solution of this conjecture. Orientations with rooted connectivity requirements will also be discussed. Joint work with D. Garamvölgyi, Cs. Király, and S. Villányi.

 

Joel Moreira (University of Warwick).

Title: The density finite sums theorem.

Abstract:

The finite sums theorem of Hindman states that for every partition of the natural numbers into finitely many pieces, there exists an infinite set B of natural numbers such that the set FS(B) of all the sums of its finite subsets is contained in a single piece. While not every set of positive density contains a configuration of the form FS(B), the quest for a satisfactory density analogue of Hindman's theorem was launched by Paul Erdős in the late 1970s. I will survey some of the results in this direction and present a recent theorem that may be seen as the possible density version of the finite sums theorem. This talk is based on joint work with Kra, Richter and Robertson.

 

The event is free to attend, but please register via this link, for catering and room-booking purposes. 

Some funding is available towards travel to support the attendance of early-career researchers (that is, PhD students and postdocs). If you wish to apply for this, please estimate the amount on the event registration form.

Supported by the Heilbronn Institute Small Grants Scheme