Add to ORKGThe existance of planar graphs with odd girth 2k + 1 and high girth that cannot be (2k + 1, k)-coloured was left as an open question by Klostermeyer and Zang. In this note we show that such graphs exist for arbitraryly large k. We also show that these graphs have fractional chromatic number greater than 2 + 1/k
AbstractErdős proved that there are graphs with arbitrarily large girth and chromatic number. We stu...
An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such tha...
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two ...
Abstract. In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that...
We prove a conjecture of Dvořák, Král, Nejedlý, and Škrekovski that planar graphs of girth at l...
Given any rational numbers $r \geq r' >2$ and an integer $g$, we prove that there is a graph $G$ of...
AbstractWe show that a planar graph with girth at least 20t−23 has circular chromatic number at most...
AbstractWe prove that for every k and every ε>0, there exists g such that every graph with tree-widt...
Reed conjectured that for every > 0 and ∆ there exists g such that the fractional total chromatic...
AbstractReed conjectured that for every ϵ>0 and Δ there exists g such that the fractional total chro...
AbstractIt is proved that ifGis a planar graph with total (vertex–edge) chromatic number χ″, maximum...
AbstractIn 1992 Gyárfás showed that a graph G having only k odd cycle lengths is (2k+1)-colourable, ...
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a ...
The focus of this thesis is star coloring planar graphs. A star coloring of a planar graph is a prop...
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two ...
AbstractErdős proved that there are graphs with arbitrarily large girth and chromatic number. We stu...
An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such tha...
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two ...
Abstract. In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that...
We prove a conjecture of Dvořák, Král, Nejedlý, and Škrekovski that planar graphs of girth at l...
Given any rational numbers $r \geq r' >2$ and an integer $g$, we prove that there is a graph $G$ of...
AbstractWe show that a planar graph with girth at least 20t−23 has circular chromatic number at most...
AbstractWe prove that for every k and every ε>0, there exists g such that every graph with tree-widt...
Reed conjectured that for every > 0 and ∆ there exists g such that the fractional total chromatic...
AbstractReed conjectured that for every ϵ>0 and Δ there exists g such that the fractional total chro...
AbstractIt is proved that ifGis a planar graph with total (vertex–edge) chromatic number χ″, maximum...
AbstractIn 1992 Gyárfás showed that a graph G having only k odd cycle lengths is (2k+1)-colourable, ...
Wang and Lih conjectured that for every g ≥ 5, there exists a number M(g) such that the square of a ...
The focus of this thesis is star coloring planar graphs. A star coloring of a planar graph is a prop...
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two ...
AbstractErdős proved that there are graphs with arbitrarily large girth and chromatic number. We stu...
An additive coloring of a graph G is a labeling of the vertices of G from {1, 2, . . . , k} such tha...
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two ...