Geodesic
Extension from precoloured sets of edges
Katherine Edwards1 ; António Girão2 ; Jan van den Heuvel3 ; Ross J. Kang4 ; Gregory J. Puleo5 ; Jean-Sébastien Sereni6
1Nokia Bell Labs
2Cambridge University
3London School of Economics
4Radboud University Nijmegen
5Auburn University
6CNRS, CSTB (ICube)
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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We consider precolouring extension problems for proper edge-colourings of graphs and multigraphs, in an attempt to prove stronger versions of Vizing's and Shannon's bounds on the chromatic index of (multi)graphs in terms of their maximum degree $\Delta$. We are especially interested in the following question: when is it possible to extend a precoloured matching to a colouring of all edges of a (multi)graph? This question turns out to be related to the notorious List Colouring Conjecture and other classic notions of choosability.
DOI : 10.37236/6303
Classification : 05C15, 05C07, 05C35
Mots-clés : edge-colouring, precolouring extension, multigraphs, list colouring

Katherine Edwards  1   ; António Girão  2   ; Jan van den Heuvel  3   ; Ross J. Kang  4   ; Gregory J. Puleo  5   ; Jean-Sébastien Sereni  6

1 Nokia Bell Labs
2 Cambridge University
3 London School of Economics
4 Radboud University Nijmegen
5 Auburn University
6 CNRS, CSTB (ICube) 
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     author = {Katherine Edwards and Ant\'onio Gir\~ao and Jan van den Heuvel and Ross J. Kang and Gregory J. Puleo and Jean-S\'ebastien Sereni},
     title = {Extension from precoloured sets of edges},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/6303},
     zbl = {1393.05115},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6303/}
}
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Katherine Edwards; António Girão; Jan van den Heuvel; Ross J. Kang; Gregory J. Puleo; Jean-Sébastien Sereni. Extension from precoloured sets of edges. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6303

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