According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable
AbstractA graph G=G(V,E) is called L-list colourable if there is a vertex colouring of G in which th...
AbstractA graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which...
AbstractTwo cycles are said to be adjacent if they share a common edge. Let G be a planar graph with...
c©2013 According to the List Colouring Conjecture, if G is a multigraph then χ′(G) = χ l(G). In this...
AbstractWe investigate structural properties of planar graphs without triangles or without 4-cycles,...
In this paper we prove that if G is a planar graph, and each 7-cycle contains at most two chords, th...
AbstractSome structural properties of planar graphs without 4-cycles are investigated. By the struct...
AbstractIt is proved that a planar graph G without five cycles is three degenerate, hence, four choo...
AbstractA graph G = G(V, E) with lists L(v), associated with its vertices v ∈ V, is called L-list co...
AbstractA graph G=G(V,E) is called L-list colourable if there is a vertex colouring of G in which th...
AbstractA graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which...
AbstractThis paper starts with a discussion of several old and new conjectures about choosability in...
AbstractA graph G = G(V, E) with lists L(v), associated with its vertices v ∈ V, is called L-list co...
We prove that graphs that can be made planar by deleting two edges are 5-choosable. To arrive at thi...
AbstractLet G be a planar graph with maximum degree Δ such that G has no cycle of length from 4 to k...
AbstractA graph G=G(V,E) is called L-list colourable if there is a vertex colouring of G in which th...
AbstractA graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which...
AbstractTwo cycles are said to be adjacent if they share a common edge. Let G be a planar graph with...
c©2013 According to the List Colouring Conjecture, if G is a multigraph then χ′(G) = χ l(G). In this...
AbstractWe investigate structural properties of planar graphs without triangles or without 4-cycles,...
In this paper we prove that if G is a planar graph, and each 7-cycle contains at most two chords, th...
AbstractSome structural properties of planar graphs without 4-cycles are investigated. By the struct...
AbstractIt is proved that a planar graph G without five cycles is three degenerate, hence, four choo...
AbstractA graph G = G(V, E) with lists L(v), associated with its vertices v ∈ V, is called L-list co...
AbstractA graph G=G(V,E) is called L-list colourable if there is a vertex colouring of G in which th...
AbstractA graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which...
AbstractThis paper starts with a discussion of several old and new conjectures about choosability in...
AbstractA graph G = G(V, E) with lists L(v), associated with its vertices v ∈ V, is called L-list co...
We prove that graphs that can be made planar by deleting two edges are 5-choosable. To arrive at thi...
AbstractLet G be a planar graph with maximum degree Δ such that G has no cycle of length from 4 to k...
AbstractA graph G=G(V,E) is called L-list colourable if there is a vertex colouring of G in which th...
AbstractA graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which...
AbstractTwo cycles are said to be adjacent if they share a common edge. Let G be a planar graph with...
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