Add to ORKGLovasz invoked topological colouring bounds in proving Kneser\u27s Conjecture. Subsequently, numerous applications of topological techniques to graph colouring problems have arisen. However, even today, little is known about how to construct a graph with a particular topological colouring bound, or about the structure of such graphs. The aim of this thesis is to remedy this deficit. First, we will perform a review of topological techniques used in bounding the chromatic number and discuss constructing graphs with particular topological colouring bounds. Then we will derive necessary conditions for a graph to attain a particular topological colouring bound, and use these conditions to analyze the structure of such graphs. In particular, we p...
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c: V → {1, 2,..., k} such ...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
AbstractIn this paper we introduce a chromatic parameter, called the fixing chromatic number, which ...
The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors t...
AbstractIn 1976, Stahl [14] defined the m-tuple coloring of a graph G and formulated a conjecture on...
The local chromatic number of a graph G is the number of colors appearing in the most colorful close...
Beginning with the origin of the four color problem in 1852, the field of graph colorings has develo...
This work.develops the foundations of topological graph theory with a unified approach using combin...
In this paper we introduce the notion of Σ-colouring of a graph G: For given subsets Σ(v) of neighbo...
The topological Tverberg theorem has been generalized in several directions by setting extra restric...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Abstract. A graph embedded in a surface with all faces of size 4 is known as a quadrangulation. We e...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c: V → {1, 2,..., k} such ...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
AbstractIn this paper we introduce a chromatic parameter, called the fixing chromatic number, which ...
The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors t...
AbstractIn 1976, Stahl [14] defined the m-tuple coloring of a graph G and formulated a conjecture on...
The local chromatic number of a graph G is the number of colors appearing in the most colorful close...
Beginning with the origin of the four color problem in 1852, the field of graph colorings has develo...
This work.develops the foundations of topological graph theory with a unified approach using combin...
In this paper we introduce the notion of Σ-colouring of a graph G: For given subsets Σ(v) of neighbo...
The topological Tverberg theorem has been generalized in several directions by setting extra restric...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Abstract. A graph embedded in a surface with all faces of size 4 is known as a quadrangulation. We e...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
For a positive integer k, a k-colouring of a graph G = (V,E) is a mapping c: V → {1, 2,..., k} such ...
Lovász's striking proof of Kneser's conjecture from 1978 using the Borsuk–Ulam theorem provides a lo...
AbstractIn this paper we introduce a chromatic parameter, called the fixing chromatic number, which ...