# Robert Hickingbotham

# Hi There!

I am a Postdoctoral Research Fellow with the MC2 team in LIP at ENS Lyon. My post-doc supervisor is Édouard Bonnet. I completed my PhD under the supervision of David R. Wood at Monash University.

Beyond my mathematical pursuits, I am an evangelical Christian and a member of Regeneration Church Monash.

Contact

Email: rd DOT hickingbotham AT gmail DOT com

Research Interests

Structural Graph Theory

Coarse Graph Theory

Graph Product Structure Theory

PhD Thesis

[23] Robert Hickingbotham. Exploring sparse and hereditary graph classes via products and tree-decompositions. PhD Thesis, School of Mathematics, Monash University, Melbourne, 2024. [publication]

Preprints

[22] Rutger Campbell, James Davies, Marc Distel, Bryce Frederickson, J. Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Sebastian Wiederrecht, David R. Wood, and Liana Yepremyan. Treewidth, Hadwiger Number, and Induced Minors. 2024. [arXiv]

[21] James Davies, Robert Hickingbotham, Freddie Illingworth, and Rose McCarty. Fat Minors Cannot be Thinned (by Quasi-Isometries). 2024. [arXiv]

[20] Marcin Briański, Robert Hickingbotham, and David R. Wood. Defective and Clustered Colouring of Graphs with Given Girth. 2023. [arXiv]

[19] Robert Hickingbotham. Cop-width, flip-width and strong colouring numbers. 2023. [arXiv]

[18] Robert Hickingbotham, Raphael Steiner, and David R. Wood. Clustered Colouring of Odd-H-Minor-Free Graphs. 2023. [arXiv]

[17] Marc Distel, Robert Hickingbotham, Michał T. Seweryn, and David R. Wood. Powers of planar graphs, product structure, and blocking partitions. 2023. [arXiv]

Journal Publications

[16] Marc Distel, Vida Dujmović, David Eppstein, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, Michał T. Seweryn, and David R. Wood. Product structure extension of the Alon--Seymour--Thomas theorem. SIAM Journal on Discrete Mathematics 38.3:2095-2107, 2024. [arXiv]

[15] Rutger Campbell, Katie Clinch, Marc Distel, J. Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, and David R. Wood. Product structure of graph classes with bounded treewidth. Combinatorics, Probability and Computing 33.3:351-376, 2024. [arXiv]

[14] Robert Hickingbotham and David R. Wood. Shallow minors, graph products and beyond planar graphs. SIAM Journal on Discrete Mathematics 38.1:1057-1089, 2024. [arXiv]

[13] Vida Dujmović, Robert Hickingbotham, Jędrzej Hodor, Gwenaël Joret, Hoang La, Piotr Micek, Pat Morin, Clément Rambaud, and David R. Wood. The Grid Minor Theorem Revisited, accepted to SODA 2024. [arXiv]

[12] Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, and David R. Wood. Treewidth, Circle Graphs and Circular Drawings. SIAM Journal on Discrete Mathematics 38.1:965-987, 2024. [arXiv]

[11] Vida Dujmović, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, and David R. Wood. The Excluded Tree Minor Theorem Revisited. Combinatorics, Probability and Computing 33.1:85-90, 2024. [arXiv]

[10] Robert Hickingbotham. Odd colourings, conflict-free colourings and strong colouring numbers. Australasian J. Combinatorics 87.1:160-164, 2023. [arXiv]

[9] Rutger Campbell, Marc Distel, J. Pascal Gollin, Daniel Harvey, Kevin Hendrey, Robert Hickingbotham, Bojan Mohar, and David R. Wood. Graphs of linear growth have bounded treewidth. Electronic J. Combinatorics 30:P3.1, 2023. [arXiv]

[8] Robert Hickingbotham and David R. Wood. Structural properties of graph products. Journal of Graph Theory, accepted in 2023. [publication] [arXiv]

[7] Robert Hickingbotham. Induced subgraphs and path decompositions. Electronic J. Combinatorics 30:P2.37, 2023. [arXiv]

[6] Robert Hickingbotham, Laura Merker, Paul Jungeblut, and David R. Wood. The product structure of squaregraphs. Journal of Graph Theory 105: 179–191, 2024. [arXiv]

[5] David Eppstein, Robert Hickingbotham, Laura Merker, Sergey Norin, Michał T. Seweryn, and David R. Wood. Three-dimensional graph products with unbounded stack-number. Discrete & Computational Geometry 71:1210-1237, 2024. [arXiv]

[4] Marc Distel, Robert Hickingbotham, Tony Huynh, and David R. Wood. Improved product structure for graphs on surfaces. Discrete Math. & Theoretical Comput. Sci. 24.2:#6, 2022. [arXiv]

[3] Vida Dujmović, David Eppstein, Robert Hickingbotham, Pat Morin, and David R. Wood. Stack-number is not bounded by queue-number. Combinatorica 42:151–164, 2022. [arXiv]

Unpublished Notes

[2] Robert Hickingbotham and David R. Wood. Structural properties of bipartite subgraphs. 2021. [arXiv]

Honour's Thesis

[1] Robert Hickingbotham. Graph minors and tree decompositions. Honour’s thesis, School of Mathematics, Monash University, Melbourne, 2019. [PDF]

Referee

I have reviewed articles for the following:

Combinatorica

Electronic Journal of Combinatorics

Transactions on Algorithms

Computing in Geometry and Topology

SOCG 2022

Algorithmica

Journal of Combinatorial Theory, Series B

Teaching

I have worked for Monash University as a sessional teaching associate in the following units:

MTH1030 - Techniques for modelling

MAT1830 - Discrete Mathematics for Computer Science

MTH2021 - Linear Algebra with Applications

MTH3170 - Network Mathematics

Conferences

I co-organised the 2020 Australasian Graduate Symposium in Combinatorics.