On optimal orientation of cycle vertex multiplications

On optimal orientations of tree vertex-multiplications

Maximizing Expectation on Vertex-Disjoint Cycle Packing

This paper proposes a method for computing the expectation for the length of the maximum set of vertex-disjoint cycles in a digraph where vertices and/or arcs are subject to failure with a known probability. This method has an immediate practical application: it can be used for the solution of a kidney exchange program in the common situation where the underlying graph is unreliable. Results fo...

On cycle packings and feedback vertex sets

For a graph G, let fvs and cp denote the minimum size of a feedback vertex set in G and the maximum size of a cycle packing in G, respectively. Kloks, Lee, and Liu conjectured that fvs(G) ≤ 2 cp(G) if G is planar. They proved a weaker inequality, replacing 2 by 5. We improve this, replacing 5 by 3, and verifying the resulting inequality for graphs embedded in surfaces of nonnegative Euler chara...

Encoding Orientation of Graphs by Vertex Labels

Let E = (V;A) be an antisymmetric directed graph, the elements of V being called labels. We say that the orientation of a directed (simple, loopless) graph H = (V;A) can be encoded by E if there exists a mapping : V ! V satisfying : 8 (x; y) 2 A; ( (x); (y)) 2 A. It has been proved that the orientation of any directed planar (resp. outerplanar, with maximal degree 3) graph can be encoded by usi...

Theoretical Investigation of Consumption Patterns Effect on Optimal Orientation of Collector in Solar Water Heating System

One of the subjects in solar water heater design is considering distribution of hot water consumption during the day. For example, each of the household, commercial, office, school, and industrial consumptions have a particular distribution of hot water consumption named pattern in this article. In solar computation principles, the effect of longitude, latitude, and altitude on collector angle ...