AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-trivial vertex partition. This is then used to show that for finite simple graphs of maximal degree Δ(G) = Δ, the list chromatic number is bounded by X|(G)⩽7Δ/4+o(Δ)
AbstractGiven a graph G and a positive integer p, χp(G) is the minimum number of colours needed to c...
This thesis focuses on generalisations of the colouring problem in various classes of sparse graphs....
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
AbstractIt is shown that the list edge chromatic number of any graph with maximal degree Δ and girth...
AbstractWe prove that, if a graph has a list of k available colors at every vertex, then the number ...
AbstractThe first author showed that the list chromatic number of every graph with average degree d ...
The chromatic polynomial of a graph $G$, denoted $P(G,m)$, is equal to the number of proper $m$-colo...
List colouring is an influential and classic topic in graph theory. We initiate the study of a natur...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
The famous List Colouring Conjecture from the 1970s states that for every graph $G$ the chromatic in...
A collection of graphs is \textit{nearly disjoint} if every pair of them intersects in at most one v...
List packing is a notion that was introduced in 2021 (by Cambie et al.). The list packing number of ...
AbstractThis paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63(1995), 1...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractGiven a graph G and a positive integer p, χp(G) is the minimum number of colours needed to c...
This thesis focuses on generalisations of the colouring problem in various classes of sparse graphs....
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
AbstractIt is shown that the list edge chromatic number of any graph with maximal degree Δ and girth...
AbstractWe prove that, if a graph has a list of k available colors at every vertex, then the number ...
AbstractThe first author showed that the list chromatic number of every graph with average degree d ...
The chromatic polynomial of a graph $G$, denoted $P(G,m)$, is equal to the number of proper $m$-colo...
List colouring is an influential and classic topic in graph theory. We initiate the study of a natur...
AbstractWe give a new upper bound on the total chromatic number of a graph. This bound improves the ...
The famous List Colouring Conjecture from the 1970s states that for every graph $G$ the chromatic in...
A collection of graphs is \textit{nearly disjoint} if every pair of them intersects in at most one v...
List packing is a notion that was introduced in 2021 (by Cambie et al.). The list packing number of ...
AbstractThis paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B63(1995), 1...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractGiven a graph G and a positive integer p, χp(G) is the minimum number of colours needed to c...
This thesis focuses on generalisations of the colouring problem in various classes of sparse graphs....
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
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