Geodesic
A note on Norine's antipodal-colouring conjecture
Vojtěch Dvořák1
1University of Cambridge
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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Norine's antipodal-colouring conjecture, in a form given by Feder and Subi, asserts that whenever the edges of the discrete cube are 2-coloured there must exist a path between two opposite vertices along which there is at most one colour change. The best bound to date was that there must exist such a path with at most $n/2$ colour changes. Our aim in this note is to improve this upper bound to $(\frac{3}{8}+o(1))n$.
DOI : 10.37236/9219
Classification : 05C15, 05C38
Mots-clés : antipodal vertices, hypercube, 2-edge coloring

Vojtěch Dvořák  1

1 University of Cambridge 
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Vojtěch Dvořák. A note on Norine's antipodal-colouring conjecture. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9219

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