In this dissertation, I will discuss two results on the oriented diameter of graphs with certain properties. In the first problem, I studied the oriented diameter of a graph G. Erdos et al. in 1989 showed that for any graph with |V | = n and δ(G) = δ the maximum the diameter could possibly be was 3 n/ δ+1. I considered whether there exists an orientation on a given graph with |G| = n and δ(G) = δ that has a small diameter. Bau and Dankelmann (2015) showed that there is an orientation of diameter 11 n/ δ+1 + O(1), and showed that there is a graph which the best orientation admitted is 3 n/ δ+1 + O(1). It was left as an open question whether the factor of 11 in the first result could be reduced to 3. The result above was improved to 7 n / δ+1...
A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is t...
This paper discusses the most popular algebraic techniques and computational methods that have been ...
AbstractLet G be a bridgeless connected undirected (b.c.u.) graph. The oriented diameter of G, OD(G)...
In this dissertation, I will discuss two results on the oriented diameter of graphs with certain pro...
AbstractIn 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has ...
AbstractIn 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has ...
A strong orientation of a graph $G$ is an assignment of a direction to each edge such that $G$ is st...
We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of ...
This is the post-print version of the Article. The official published version can be accessed from t...
The diameter of a directed graph is the maximum of the lengths of the shortest paths between all pai...
AbstractIn this note, we use a technique introduced by Dankelmann and Entringer [P. Dankelmann, R.C....
AbstractLet D be a strongly connected oriented graph, i.e., a digraph with no cycles of length 2, of...
Robbins 研究單行道問題時,證明了一個連通圖有強定向的充分必要條件是此圖中沒有橋。除了強定向的存在性之外,一個有趣且實際的問題是,這些強定向的最小直徑的長度為何? 更精確地說,對於一個給定的圖 ...
AbstractFor a graph G, let ε(G) denote the minimum value of the diameters diam D of D, where D runs ...
The first part of this dissertation discussing the problem of bounding the diameter of a graph in te...
A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is t...
This paper discusses the most popular algebraic techniques and computational methods that have been ...
AbstractLet G be a bridgeless connected undirected (b.c.u.) graph. The oriented diameter of G, OD(G)...
In this dissertation, I will discuss two results on the oriented diameter of graphs with certain pro...
AbstractIn 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has ...
AbstractIn 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has ...
A strong orientation of a graph $G$ is an assignment of a direction to each edge such that $G$ is st...
We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of ...
This is the post-print version of the Article. The official published version can be accessed from t...
The diameter of a directed graph is the maximum of the lengths of the shortest paths between all pai...
AbstractIn this note, we use a technique introduced by Dankelmann and Entringer [P. Dankelmann, R.C....
AbstractLet D be a strongly connected oriented graph, i.e., a digraph with no cycles of length 2, of...
Robbins 研究單行道問題時,證明了一個連通圖有強定向的充分必要條件是此圖中沒有橋。除了強定向的存在性之外,一個有趣且實際的問題是,這些強定向的最小直徑的長度為何? 更精確地說,對於一個給定的圖 ...
AbstractFor a graph G, let ε(G) denote the minimum value of the diameters diam D of D, where D runs ...
The first part of this dissertation discussing the problem of bounding the diameter of a graph in te...
A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is t...
This paper discusses the most popular algebraic techniques and computational methods that have been ...
AbstractLet G be a bridgeless connected undirected (b.c.u.) graph. The oriented diameter of G, OD(G)...