Adapting Search Theory to Networks

The CSE is interested in the general problem of locating objects in networks. Because of their exposure to search theory, the problem they brought to the workshop was phrased in terms of adapting search theory to networks. Thus, the first step was the introduction of an already existing healthy literature on searching graphs. T. D. Parsons, who was then at Pennsylvania State University, was approached in 1977 by some local spelunkers who asked his aid in optimizing a search for someone lost in a cave in Pennsylvania. Parsons quickly formulated the problem as a search problem in a graph. Subsequent papers led to two divergent problems. One problem dealt with searching under assumptions of fairly extensive information, while the other problem dealt with searching under assumptions of essentially zero information. These two topics are developed in the next two sections

Edge-pancyclic block-intersection graphs

AbstractIt is shown that the block-intersection graph of both a balanced incomplete block design with block size at least 3 and λ = 1, and a transversal design is edge-pancyclic

On The 2-Spanning Cyclability Of Honeycomb Toroidal Graphs

A graph $X$ is 2-spanning cyclable if for any pair of distinct vertices $u$ and $v$ there is a 2-factor of $X$ consisting of two cycles such that $u$ and $v$ belong to distinct cycles. In this paper we examine the 2-spanning cyclability of honeycomb toroidal graphs.Comment: 17 pages, 2 figure

Searching and sweeping graphs: a brief survey

This papers surveys some of the work done on trying to capture an intruder in a graph. If the intruder may be located only at vertices, the term searching is employed. If the intruder may be located at vertices or along edges, the term sweeping is employed. There are a wide variety of applications for searching and sweeping. Old results, new results and active research directions are discussed

Sweeping graphs with large clique number

AbstractSearching a network for intruders is an interesting and often difficult problem. Sweeping (or edge searching) is one such search model, in which intruders may exist anywhere along an edge. It was conjectured that graphs exist for which the connected sweep number is strictly less than the monotonic connected sweep number. We prove that this is true, and the difference can be arbitrarily large. We also show that the clique number is a lower bound on the sweep number

On factorisations of complete graphs into circulant graphs and the Oberwolfach problem

Various results on factorisations of complete graphs into circulant graphs and on 2-factorisations of these circulant graphs are proved. As a consequence, a number of new results on the Oberwolfach Problem are obtained. For example, a complete solution to the Oberwolfach Problem is given for every 2-regular graph of order 2p where p ≡ 5 (mod 8) is prime