# Robert Hickingbotham

# Hi There!

I am a PhD student in the Discrete Mathematics Research Group at Monash University. My supervisor is David R. Wood. I received my undergraduate degree at Monash University, where I completed my Honour's project in structural graph theory with the same supervisor. I was awarded the CMSA Anne Penfold Street Student Prize for the best student talk at the 44ACC. I co-organise the seminars for the Monash Discrete Maths Research Group. Details for upcoming talks can be viewed here.

Beyond my mathematical pursuits, I am an evangelical Christian and serve as an elder at Regeneration Church Monash.

Research Interests

Structural Graph Theory

Linear Layouts of Graphs

Graph Product Structure Theory

Graph Colouring

Preprints

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

[20] Marcin Briański, Robert Hickingbotham, 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, David R. Wood. Clustered Colouring of Odd-H-Minor-Free Graphs. 2023. [arXiv]

[17] Marc Distel, Robert Hickingbotham, Michał T. Seweryn, 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, David R. Wood. Product structure extension of the Alon--Seymour--Thomas theorem. SIAM Journal on Discrete Mathematics, accepted in 2024. [arXiv]

[15] Rutger Campbell, Katie Clinch, Marc Distel, J. Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, David R. Wood. Product structure of graph classes with bounded treewidth. Combinatorics, Probability and Computing, accepted in 2023. [arXiv]

[14] Robert Hickingbotham and David R. Wood. Shallow minors, graph products and beyond planar graphs. SIAM Journal on Discrete Mathematics, accepted in 2023. [arXiv]

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

[12] Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood. Treewidth, Circle Graphs and Circular Drawings. 2022. SIAM Journal on Discrete Mathematics, accepted in 2023. [arXiv]

[11] Vida Dujmović, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, David R. Wood. The Excluded Tree Minor Theorem Revisited. Combinatorics, Probability and Computing, accepted in 2023. [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, 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, accepted in 2023. [publication] [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, accepted in 2022. [publication] [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:

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.

Contact

Email: robert DOT hickingbotham AT monash DOT edu