Changes
Created page with '==Node-colouring== A '''k-colouring''' of a graph ''G=(V,E)'' is a partitioning of ''V'' into ''k'' stable sets. The '''colouring number''' of ''G'', usually denoted by <math>\c…'
==Node-colouring==
A '''k-colouring''' of a graph ''G=(V,E)'' is a partitioning of ''V'' into ''k'' stable sets. The '''colouring number''' of ''G'', usually denoted by <math>\chi(G)</math>, is the smallest integer ''k'' for which ''G'' has a ''k''-colouring.
==Edge-colouring==
A '''k-edge-colouring''' of a graph ''G=(V,E)'' is a partitioning of ''E'' into ''k'' matchings. The '''edge-colouring number''' of ''G'' is the smallest integer ''k'' for which ''G'' has a ''k''edge--colouring.
A graph ''G=(V,E)'' is '''k-list-edge-colourable''' if for arbitrary sets <math>L_e</math> of size ''k'' for every <math>e \in E</math>, we can choose <math>c_e \in L_e</math> for every <math>e \in E</math> such that <math>c_e \neq c_f</math> if ''e'' and ''f'' have a common end-node.
The '''list-edge-colouring number''' of a graph is the smallest integer ''k'' for which it is ''k''-list-edge-colourable.
[[Category:Definitions]]
A '''k-colouring''' of a graph ''G=(V,E)'' is a partitioning of ''V'' into ''k'' stable sets. The '''colouring number''' of ''G'', usually denoted by <math>\chi(G)</math>, is the smallest integer ''k'' for which ''G'' has a ''k''-colouring.
==Edge-colouring==
A '''k-edge-colouring''' of a graph ''G=(V,E)'' is a partitioning of ''E'' into ''k'' matchings. The '''edge-colouring number''' of ''G'' is the smallest integer ''k'' for which ''G'' has a ''k''edge--colouring.
A graph ''G=(V,E)'' is '''k-list-edge-colourable''' if for arbitrary sets <math>L_e</math> of size ''k'' for every <math>e \in E</math>, we can choose <math>c_e \in L_e</math> for every <math>e \in E</math> such that <math>c_e \neq c_f</math> if ''e'' and ''f'' have a common end-node.
The '''list-edge-colouring number''' of a graph is the smallest integer ''k'' for which it is ''k''-list-edge-colourable.
[[Category:Definitions]]
