# 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.

Research Interests

Structural Graph Theory

Linear Layouts of Graphs

Graph Product Structure Theory

Graph Colouring

Preprints

[15] Vida Dujmović, Robert Hickingbotham, Gwenaël Joret, Piotr Micek, Pat Morin, David R. Wood. The Excluded Tree Minor Theorem Revisited. 2023. [arXiv]

[14] Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood. Treewidth, Circle Graphs and Circular Drawings. 2022. [arXiv]

[13] Marc Distel, Vida Dujmović, David Eppstein, Robert Hickingbotham, Gwenaël Joret, Pat Morin, Michał T. Seweryn, David R. Wood. Graphs excluding a fixed minor are O(\sqrt{n})-complete-blowups of a treewidth 4 graph. 2022. [arXiv]

[12] 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. 2022. [arXiv]

[11] Robert Hickingbotham. Odd colourings, conflict-free colourings and strong colouring numbers. 2022. [arXiv]

[10] Robert Hickingbotham and David R. Wood. Shallow minors, graph products and beyond planar graphs. 2021. [arXiv]

Journal Publications

[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 Journal of Combinatorics, accepted in 2023. [arXiv]

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

[7] Robert Hickingbotham. Induced subgraphs and path decompositions. Electronic Journal of Combinatorics, accepted in 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. [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. [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

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