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5-Choosability of Planar-plus-two-edge Graphs

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Mahmoud_Amena.pdf (558.96 KB)

Date

2018-01-02

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Mahmoud, Amena

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University of Waterloo

Abstract

We prove that graphs that can be made planar by deleting two edges are 5-choosable. To arrive at this, first we prove an extension of a theorem of Thomassen. Second, we prove an extension of a theorem Postle and Thomas. The difference between our extensions and the theorems of Thomassen and of Postle and Thomas is that we allow the graph to contain an inner 4-list vertex. We also use a colouring technique from two papers by Dvořák, Lidický and Škrekovski, and independently by Compos and Havet.

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http://hdl.handle.net/10012/12798

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Combinatorics and Optimization