The choice number of a graph G, denoted ch(G), is the minimum integer k such that for any assignment of lists of size k to the vertices of G, there is a proper colouring of G such that every vertex is mapped to a colour in its list. For general graphs, the choice number is not bounded above by a function of the chromatic number.In this thesis, we prove a conjecture of Ohba which asserts that ch(G) = χ(G) whenever |V (G)| ≤ 2χ(G) + 1. We also prove a strengthening of Ohba's Conjecture which is best possible for graphs on at most 3χ(G) vertices, and pose several conjectures related to our work.Le nombre de choix d'un graphe G, noté ch(G), est le plus petit entier k tel que pour toute affectation de listes de taille k au sommets de G, il y a u...
Erdos, Rubin and Taylor showed in 1979 that for any connected graph G which is not a complete graph ...
A proper coloring of a graph is an assignment of colors to the vertices so that no two adjacent vert...
AbstractThis paper starts with a discussion of several old and new conjectures about choosability in...
c©Jonathan A. Noel, 2013 The choice number of a graph G, denoted ch(G), is the minimum integer k suc...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Let ch(G) denote the choice number of a graph G (also called “list chromatic num-ber ” or “choosabil...
AbstractA graph G is said to be chromatic-choosable if its choice number is equal to its chromatic n...
AbstractA graph G is called chromatic-choosable if its choice number is equal to its chromatic numbe...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Suppose ch(G) and X(G) denote, respectively, the choice number and the chromatic number of a graph G...
A list colouring problem asks the following: given an assignment of lists L(v) of colours to each ve...
AbstractA graph G is said to be chromatic-choosable if ch(G)=χ(G). Ohba has conjectured that every g...
AbstractOhba has conjectured that if G is a k-chromatic graph with at most 2k+1 vertices, then the l...
AbstractOne of the authors has conjectured that every graph G with 2χ(G)+1 or fewer vertices is χ(G)...
Erdos, Rubin and Taylor showed in 1979 that for any connected graph G which is not a complete graph ...
A proper coloring of a graph is an assignment of colors to the vertices so that no two adjacent vert...
AbstractThis paper starts with a discussion of several old and new conjectures about choosability in...
c©Jonathan A. Noel, 2013 The choice number of a graph G, denoted ch(G), is the minimum integer k suc...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Let ch(G) denote the choice number of a graph G (also called “list chromatic num-ber ” or “choosabil...
AbstractA graph G is said to be chromatic-choosable if its choice number is equal to its chromatic n...
AbstractA graph G is called chromatic-choosable if its choice number is equal to its chromatic numbe...
Let ch(G) denote the choice number of a graph G (also called “list chromatic number” or “choosabilit...
Suppose ch(G) and X(G) denote, respectively, the choice number and the chromatic number of a graph G...
A list colouring problem asks the following: given an assignment of lists L(v) of colours to each ve...
AbstractA graph G is said to be chromatic-choosable if ch(G)=χ(G). Ohba has conjectured that every g...
AbstractOhba has conjectured that if G is a k-chromatic graph with at most 2k+1 vertices, then the l...
AbstractOne of the authors has conjectured that every graph G with 2χ(G)+1 or fewer vertices is χ(G)...
Erdos, Rubin and Taylor showed in 1979 that for any connected graph G which is not a complete graph ...
A proper coloring of a graph is an assignment of colors to the vertices so that no two adjacent vert...
AbstractThis paper starts with a discussion of several old and new conjectures about choosability in...