Add to ORKGCranston and Kim conjectured that if G is a connected graph with maximum degree ∆ and G is not a Moore Graph, then χ`(G 2) ≤ ∆2 − 1; here χ ` is the list chromatic number. We prove their conjecture; in fact, we show that this upper bound holds even for online list chromatic number. MSC: 05C15, 05C35
A list colouring problem asks the following: given an assignment of lists L(v) of colours to each ve...
AbstractThe1999 Academic Pressentire chromatic number χCopyright vef(G) of a plane graphGis the leas...
Vizing’s Theorem states that any graph G has chromatic index either the maximum degree Δ(G) or Δ(G) ...
Cranston and Kim conjectured that if G is a connected graph with maximum degree ∆ and G is not a Moo...
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with max...
The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent...
Let G be a planar graph without 4-cycles and 5-cycles and with maximum degree ∆ ≥ 32. We prove that...
In this article we discuss the current results on the list chromatic conjecture and prove that if G ...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
Kostochka and Woodall (2001) conjectured that the square of every graph has the same chromatic numbe...
A list colouring problem asks the following: given an assignment of lists L(v) of colours to each ve...
AbstractThe1999 Academic Pressentire chromatic number χCopyright vef(G) of a plane graphGis the leas...
Vizing’s Theorem states that any graph G has chromatic index either the maximum degree Δ(G) or Δ(G) ...
Cranston and Kim conjectured that if G is a connected graph with maximum degree ∆ and G is not a Moo...
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with max...
The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent...
Let G be a planar graph without 4-cycles and 5-cycles and with maximum degree ∆ ≥ 32. We prove that...
In this article we discuss the current results on the list chromatic conjecture and prove that if G ...
Let G be a claw-free graph on n vertices with clique number ω, and consider the chromatic number χ(G...
AbstractFor large values of Δ, it is shown that all Δ-regular finite simple graphs possess a non-tri...
Let G be a graph and let s be the maximum number of vertices of the same degree, each at least (∆(G)...
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $...
AbstractIt was conjectured by Reed [B. Reed, ω,α, and χ, Journal of Graph Theory 27 (1998) 177–212] ...
AbstractA well-established generalization of graph coloring is the concept of list coloring. In this...
Kostochka and Woodall (2001) conjectured that the square of every graph has the same chromatic numbe...
A list colouring problem asks the following: given an assignment of lists L(v) of colours to each ve...
AbstractThe1999 Academic Pressentire chromatic number χCopyright vef(G) of a plane graphGis the leas...
Vizing’s Theorem states that any graph G has chromatic index either the maximum degree Δ(G) or Δ(G) ...