List colouring conjecture For any graph G, ch'(G)=x'(G) However, the conjecture remains open for K2 Haggkvist-Janssen(1997) ch'(Kn)≤n If n is odd, then ch'(K Uwe Schatz(2014) If p is a prime, n= p-1, then ch'(K, )=n-1
List colouring conjecture: For any graph G, ch'(G) = '(G) However, the conjecture remains open for K 2n Haggkvist-Janssen (1997) ch'(Kn ) n Uwe Schauz (2014) If n is odd,then ch'(K n ) = n If p is a prime, n = p - 1,then ch'(K n ) = n − 1
A scheduling problem There are six teams, each needs to compete with all the others Each team can play one game per day Each team can choose one day off How many days are needed to schedule all the games? Answer: days The choices are made before the scheduling 7 days are enough
There are six teams, each needs to compete with all the others. Each team can play one game per day How many days are needed to schedule all the games? Answer: 5 days Each team can choose one day off 7 days are enough The choices are made before the scheduling A scheduling problem
A scheduling problem There are six teams, each needs to compete with all the others Each team can play one game per day Each team is allowed not to show up for one day How many days are needed to schedule all the games? On each day we know which teams havent shown up today 7 days are enough but we do not know which teams will not show up tomorrow <We need to schedule the games for today we
There are six teams, each needs to compete with all the others. Each team can play one game per day How many days are needed to schedule all the games? 7 days are enough Each team can choose one day off A scheduling problem is allowed not to show up for one day On each day, we know which teams haven’t shown up today but we do not know which teams will not show up tomorrow We need to schedule the games for today
On-line list colouring of graphs We start colouring the graph before having the full information of the list
On-line list colouring of graphs We start colouring the graph before having the full information of the list
f:I(G)→012,… f(x) is the number of permissible colours for x f-painting game(on-line list colouring game) on G Each vertex v is given f(v) tokens. Each token represents a permissible colour But we do not know yet what is the colour Two Players ister Painter 不 eveals the II Colours vertices
f-painting game (on-line list colouring game) on G f : V(G) →0,1,2, f (x) is the number of permissible colours for x Two Players: Lister Painter Each vertex v is given f(v) tokens. Each token represents a permissible colour. But we do not know yet what is the colour. Reveals the list Colours vertices