On the Number of α-Orientations (2008)
Stefan Felsner, Florian Zickfeld
We deal with the asymptotic enumeration of combinatorial structures on planar maps. Prominent instances of such problems are the enumeration of spanning trees, bipartite perfect matchings, and ice...
Spanning Trees with Many Leaves in Graphs without Diamonds and Blossoms (2007)
Bonsma, Paul, Zickfeld, Florian
It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4+2 leaves and that this can be improved to (n+4)/3 for cubic graphs without the diamond K_4-e...
Schnyder Woods and Orthogonal Surfaces (2007)
Felsner, Stefan, Zickfeld, Florian
In this paper we study connections between Schnyder woods and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and dimension theory....
Schnyder Woods and Orthogonal Surfaces (2007)
Felsner, Stefan, Zickfeld, Florian
In this paper we study connections between Schnyder woods and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and dimension theory....
Spanning trees with many leaves in graphs without diamonds and blossoms (2007)
It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4 + 2 leaves and that this can be improved to (n + 4)/3 for cubic graphs without the diamond...
Schnyder woods and orthogonal surfaces (2006)
Stefan Felsner, Florian Zickfeld
Abstract. In this paper we study connections between Schnyder woods and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and dimension...
Schnyder woods and orthogonal surfaces (2006)
Stefan Felsner, Florian Zickfeld
In this paper we study connections between planar graphs, Schnyder woods, and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and the...
On the Structure of Counterexamples to the Coloring Conjecture of Hajs (2004)
Hajs conjectured that, for any positive integer k, every graph containing no K_(k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajs' conjecture...
On the Structure of Counterexamples to the Coloring Conjecture of Hajós (2004)
Hajós conjectured that, for any positive integer k, every graph containing no K_(k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajós'...
On the Structure of Counterexamples to the Coloring Conjecture of Hajós (2004)
Hajós conjectured that, for any positive integer k, every graph containing no K_(k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajós'...
On the Structure of Counterexamples to the Coloring Conjecture of Hajós (2004)
Hajós conjectured that, for any positive integer k, every graph containing no K_(k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajós'...
On the structure of counterexamples to the coloring conjecture of Hajós (2004)
Thesis (M.S.)--School of Mathematics, Georgia Institute of Technology, 2005. Directed by Xingxing Yu.
Hajós conjectured that, for any positive integer k, every graph containing no K(̲k+1)-subdivision is k-colorable. This is true when k is at most three, and false when k exceeds six. Hajós'...
On the structure of counterexamples to the coloring conjecture of Hajós (2004)
Thesis (M.S.)--School of Mathematics, Georgia Institute of Technology, 2005. Directed by Xingxing Yu.
Reducing Hajós ’ coloring conjecture to 4-connected graphs (2004)
Hajós conjectured that, for any positive integer k, every graph containing no Kk+1-subdivision is k-colorable. This is true when k ≤ 3, and false when k ≥ 6. Hajós ’ conjecture remains open...