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Planar graphs without 3-cycles and with 4-cycles far apart are 3-choosable

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Sullivan_Matthew.pdf (365.07 KB)

Date

2016-09-16

Authors

Sullivan, Matthew

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University of Waterloo

Abstract

A graph G is said to be L-colourable if for a given list assignment L = {L(v)|v ∈ V (G)} there is a proper colouring c of G such that c(v) ∈ L(v) for all v in V (G). If G is L-colourable for all L with |L(v)| ≥ k for all v in V (G), then G is said to be k-choosable. This paper focuses on two different ways to prove list colouring results on planar graphs. The first method will be discharging, which will be used to fuse multiple results into one theorem. The second method will be restricting the lists of vertices on the boundary and applying induction, which will show that planar graphs without 3- cycles and 4-cycles distance 8 apart are 3-choosable.

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Keywords

Graph Theory, Graph Colouring

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URI

http://hdl.handle.net/10012/10859

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Theses
Combinatorics and Optimization