Discrete Mathematics

This week, several group members are attending the MATRIX workshop Extremal Problems in Graphs, Designs, and Geometries organised by Daniel Horsley, Anita Liebenau (UNSW) and Tibor Szabo (Freie Universitat Berlin).

Visitors this week include Padraig Ó Catháin from Dublin City University and Tibor Szabó from Freie Universität Berlin.

This week Heiko, Santiago, Tomasz and Melissa are co-organisers of the 7th Australian Algebra Conference, held at Monash.

Some recent papers by group members:

Anita Liebenau, Nick Wormald
Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph
J. European Math. Society 2023

Vida Dujmović, Louis Esperet, Pat Morin, David R. Wood.
Proof of the clustered Hadwiger conjecture
Proc. 64th IEEE Symposium on Foundations of Computer Science (FOCS ’23)

Aidan R. Gentle, Ian M. Wanless
On perfect sequence covering arrays
Annals Comb. 2023

Alexander Cant, Heiko Dietrich, Bettina Eick, and Tobias Moede.
Galois trees in the graph of p-groups of maximal class.
J. Algebra 2022.

Anita Liebenau, Nick Wormald
Asymptotic enumeration of digraphs and bipartite graphs by degree sequence
Random Structures Algorithms 2023

Vida Dujmović, Pat Morin, David R. Wood.
Graph product structure for non-minor-closed classes
J. Combinatorial Theory Series B 2023

Catherine Greenhill, Mikhail Isaev, Tamás Makai, Brendan D. McKay
Degree sequences of sufficiently dense random uniform hypergraphs
Combin. Probab. Comput. 2023

David Eppstein, Robert Hickingbotham, Sergey Norin, Laura Merker, Michal T. Seweryn, David R. Wood.
Three-dimensional graph products with unbounded stack-number
Discrete & Computational Geometry 2023

Ajani De Vas Gunasekara, Daniel Horsley
An Evans-style result for block designs
SIAM J. Discrete Math. 2022

Timothy C. Burness, Melissa Lee
On the classification of extremely primitive affine groups
Israel J. Math. 2023

Antonio Girão, Freddie Illingworth, Alex Scott, David R. Wood.
Defective colouring of hypergraphs
Random Structures Algorithms, 2023

The group once again featured in the Research Magazine of The Australian newspaper today.

Discrete Mathematics
Lead institution: Monash
Field leader: David Wood

Theoretical Computer Science
Lead institution: Monash
Field leader: Nick Wormald

Pure & Applied Mathematics
Lead institution: Monash
Field leader: David Wood

This week, Gabriel Verret from the University of Auckland is visiting Melissa Lee.

Group members were successful in today’s announcement of ARC Discovery Projects:

Fractional decomposition of graphs and the Nash-Williams conjecture. Daniel Horsley, Darryn Bryant (U. Queensland), Barbara Maenhaut (U. Queensland), Peter Dukes (U. Vic.).

The Global Structure of Sparse Networks. David Wood, Vida Dujmović (U. Ottawa).

This week Graham Farr is co-organising with Jo Ellis-Monaghan (Universiteit van Amsterdam), Iain Moffatt (Royal Holloway, University of London) and Kerri Morgan (RMIT University) the MATRIX program Workshop on Uniqueness and Discernment in Graph Polynomials. Jo and Iain will be visiting Monash afterwards.

Welcome to Abdul Basit, who is a new post-doctoral researcher in the Monash Discrete Mathematics Research Group, funded under Daniel Horsley’s ARC grant. Basit’s research interests include combinatorial geometry, extremal and probabilistic graph theory, and additive combinatorics.

PhD students in the discrete maths group have recently written the following single-authored papers (in addition to several multi-authored papers):

Jack Allsop, “Cycles of quadratic Latin squares and anti-perfect 1-factorisations”, J. Combin. Des. 31, (2023), 447-475

Marc Distel, “Proper Minor-Closed Classes of Graphs have Assouad-Nagata Dimension 2”, arXiv:2308.10377

Robert Hickingbotham, “Induced subgraphs and path decompositions”, Electronic J. Combinatorics 30:P2.37, 2023.

Robert Hickingbotham, “Odd colourings, conflict-free colourings and strong colouring numbers”. Australasian J. Combinatorics, accepted 2023. arXiv:2203.10402